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Phylogeny.sla
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<ITEXT CAB="1" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="44" CULP="-0.1" CH="A Visual Expedition Inside the Linux File Systems" CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="6" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="20" CULP="-0.1" CH="1. Introduction" CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="6" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="20" CULP="-0.1" CH="2. Linux Kernel 2.6.29 + tux3" CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="In this section we are going to explore a certain version of the Linux Kernel, the tux3 branch from March 14, 2009. This version contains the Linux tree up to March 10. The 2.6.29 was released on March 23 so this is not exactly the final version. I picked it because it contains btrfs and, at the time of writing this report, it is the latest one that was published by Daniel Phillips, the creator of the tux3.The rest of this section is made up exclusively of figures accompanied by extensive captions." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="1" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="10" CULP="-0.1" CH="I photograph to see what the world looks like in photographs." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Italic" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="1" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="10" CULP="-0.1" CH="—Garry Winogrand (1928–1984)" CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Map of the external symbols." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" This plot shows the external symbols for 55 kernel modules from the tux3 git repository. Each tick represents an external symbol. The file systems are show in alphabetical order. The big compact chunks of external symbols related to jbd and jbd2 are visible for ext3 and ext4. The fact that ocfs2 is also making use of jbd2 is also noticeable. Later in this section we will see how this representation looks when is reorganized based on similarities between file systems. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Number of external symbols." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" This plot shows the ranking of the file systems based on the number of external symbols. We can see that the range is about 300 symbols and there are no sudden jumps: some sizes are more popular than others but overall the space is filled quite smoothly. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Number of external symbols by categories." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" This is the same plot as the previous one except this time the file systems are grouped in categories.The first group, which contains the disk-based file systems, is led by ext4 which is ahead of xfs by 45 external symbols. Note that the number of external symbols for both ext4 and ext3 is boosted by the fact the journaling part not implemented internally but provided by jbd2 and jbd respectively. At the other end of the scale is a group of 4 file systems out of which only two, freevxfs and qnx4 are truly self-contained. The other two, msdos and vfat are getting most of their functionality from the fat module which is more than twice of their size.The second group contains the file systems dedicated to optical mediums and it holds no surprises: udf is ahead of isofs by a comfortable margin.The same thing is also true for the the third group, of the flash-based file systems, where the first place is taken by ubifs followed by jffs2. The third placed is secured by squashfs while the bottom is shared by cramfs and romfs which are separated by only 5 symbols.The fourth group is the one dedicated to the network file systems. Here the first two spots are taken by nfs and nfsd, which provide kernel support for NFS client and NFS server. On the next two places, at very close distance between them, are kafs, the Andrew File System, and cifs. The end is shared by coda and 9p.The fifth group contains, in this order, the only two cluster-based file systems: ocfs2 and gfs2. The number of external symbols for ocfs2 is increased due to the use of the jbd2 journaling library.The sixth group, the one dedicated to memory-based file systems is dominated authoritatively by proc which has almost 100 more external symbols than fuse, the file system from the second place. As expected, at the bottom sits ramfs.The seventh and last group is dedicated to ancient file systems. The first place is shared by hfs and ufs. Quite surprising, this is only one of the three ties in this group, the other two being hpfs/minix and adfs/bfs. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="The 50 most popular external symbols." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" The symbols are sorted in the descending order of their frequency while the file systems are sorted in the descending order of number of external symbols they use." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="0" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="" CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="The first two symbols are used by the function tracer. On the third place we have a tie between kfree, which is used by everybody except by ramfs, msdos and romfs, and kprintf which, surprising, is avoided by vfat, ramfs and msdos.As expected, the kmem operations are among the most popular one. So are the some basic operations like strlen, memcmp and strsep.Another thing we can notice are some (expected) pairs of calls that are always used together: register_filesystem/unregister_filesystem, _spin_lock/_spin_unlock and kmap/kunmap.Another (again expected) observation is that the lack of (un)register_filesystem identifiers in the modules which only provides services to others: dlm, lockd, fat, and jbd2/jbd2. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Heatmap of the Hamming distances." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" If we think of each file systems as a string of bits with one indicating the presence of a certain external symbol and zero as the absence of it then the Hamming distance is the minimum number of substitutions necessary to change one string into another. The heatmap is symmetric. The red indicates a Hamming distance of zero, which corresponds to maximum similarity, and yellow indicates very little similarity. Everyone is similar with itself so the diagonal is red. In this plot the file systems are sorted in ascending order of their number of external symbols. What we are going to do next is to reorder the rows and columns in a way that brings closer the file systems that are similar. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Hierarchical clustering." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" As the name implies, hierarchical clustering builds a hierarchy of clusters. There are two ways to do this: one is to start from bottom, with all the data points as clusters and then, at each step, merge two of them. This is also know as agglomerative nesting. The other one is called divisive and starts from top, with everything in a big cluster, and at each steps performs a split." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="0" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="" CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="At the right is an example of clustering 11 points situated in a 2D plane. Left is a dendrogram, a tree diagram usually used to represent the result of a hierarchical clustering. Right is a a representation using nested clusters. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Single linkage." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" When all the clusters only contains one point we can easily define the distance between them as the distance (d) between the respective points. After each merge operation we need a way to define the distance (D) between this new cluster and all the old ones. One way to do this is to consider the distance between two clusters as the minimum distance between any pair of nodes with one node in a cluster and another one in the other. Formally we could express this as D(A,B) = { min(d(x,y)) | x in A and y in B }.This method is best suited for constructing elongated clusters like the ones int he right." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Despite being a very important part of any operating system, file systems tend to get little attention. Linux has three editions for Linux Device Drivers, another three for Understanding the Linux Kernel and two for Linux Kernel Development. For the 2.4 networking stack there is Linux Networking Architecture by Klaus Wehrle et al. and for the memory subsystem there is Understanding the Linux Virtual Memory Manager by Mel Gorman. The aptly named UNIX Filesystems: Evolution, Design, and Implementation is only giving a general overview of how things work. Practical File System Design with the Be File System by Dominic Giampaolo is an an enjoyable read but, as the name indicates, it only deals with BeFS. The same is also true for HFS+ in the very thick but also very interested Mac OS X Internals: A Systems Approach by Amit Singh. I really hope that someday somebody will spend some time and put together a nice book or website in which file systems, new and old, are presented and analyzed in detail.As the disclaimer from the front page says, I don't know as much as I want about file systems. I'm making progress in learning about them in the traditional way of playing and understanding the existing code. What I'm attempting in this project is to complement this by a visual approach in which the main purpose is to try to graphically depict some the ways the things go. The main observable thing I'm using is the external symbols used by kernel modules. There are two main reasons for doing this. First, many operating systems build their file systems as kernel modules. This is useful because it separates the part we are interested in from the rest of kernel. And second, because the modules need to be loaded dynamically, the functions they call and data they access from the kernel show up as external (unresolved) symbols in their binaries. These can be easily extracted using nm. One drawback of this approach is represented by the chains of calls like the ones in the figure from below. Luckily, in the Linux kernel many functions are explicitly marked as inline so this case might not occur so frequently. I haven't check explicitly for this yet to but it is something I would like to do.That being said, here is a quick overview of the next sections. The following two are the big ones. The first is a detail analysis of one particular Linux Kernel tree and the second is a shorter one done over a large number of file systems from Linux Kernel 2.6.0 to 2.6.29. After that there is a small section that shows some aspects of the BSD family. After conclusions there is an appendix consisting of three things: the first one explains how the file systems for Linux were compiled, the second one shows timelines for the releases of Linux Kernel, FreeBSD, NetBSD and OpenBSD; the last is a detailed map of the external symbols of the kernel modules analyzed in the second section.On more thing. The figures are accompanied by captions which describe the plot and note some of the interesting things that are going on there. If you find any mistake please let me know and I'll try to fix it.Happy reading/viewing!" CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Chain of calls problem." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" Module 1 and Module 2 are two kernel modules and f1 and f2 are two functions exported by the kernel. Even f1 are two f2 different calls they are in fact closely related to each other. This is not captured by the relations between the modules and the kernel and can only be detected by also looking the way things happen inside the kernel. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Complete linkage." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" In this case the distance between clusters is defined as the maximum distance between the pairs of nodes which contain one node from one cluster and one from the other. Similar with the previous case, this could be express as D(A,B) = { max(d(x,y)) | x in A and y in B }. This method is capable of creating small and compact clusters. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<PAGEOBJECT OnMasterPage="" BottomLine="0" REXTRA="0" ALIGN="0" gHeight="970" gWidth="1.4822e-323" LANGUAGE="English" NUMPO="16" PLINEART="1" TXTSCALE="100" RightLine="0" LOCALSCX="1" LINESP="14.4" ROT="0" TXTSHX="5" TXTSTROKE="Black" WIDTH="144" ImageRes="1" GROUPS="" LOCKR="0" IFONT="Times New Roman Regular" LOCALSCY="1" NAMEDLST="" TXTSHY="-5" isInline="0" AUTOTEXT="0" FLIPPEDV="0" PCOLOR="None" RADRECT="0" REVERS="0" PRINTABLE="1" RATIO="1" FLIPPEDH="0" COLGAP="14.4" PCOLOR2="None" NEXTITEM="-1" NUMGROUP="0" TransValue="0" PLINEEND="0" TXTSTW="-0.1" FRTYPE="0" PTYPE="4" ImageClip="" isTableItem="0" TEXTFLOW2="0" SHADE2="100" TXTBASE="0" PWIDTH="1" HEIGHT="87" DASHOFF="0" PFILE2="" PFILE="" TEXTFLOW3="0" ISIZE="12" PLTSHOW="0" LINESPMode="0" TXTSTYLE="0" CLIPEDIT="0" BACKITEM="-1" TransValueS="0" EMBEDDED="1" PFILE3="" ANNAME="" SHADE="100" TXTULP="-0.1" fillRule="1" COCOOR="0 0 0 0 144 0 144 0 144 0 144 0 144 87 144 87 144 87 144 87 0 87 0 87 0 87 0 87 0 0 0 0 " BASEOF="0" PICART="1" TXTKERN="0" COLUMNS="1" OwnPage="10" LAYER="0" BOOKMARK="0" gYpos="4.4135e-260" startArrowIndex="0" TopLine="0" LOCK="0" EPROF="" gXpos="5.35105e-315" DASHS="" IRENDER="1" TEXTFLOW="0" TXTFILLSH="100" YPOS="4432.02" ANNOTATION="0" LOCALX="0" GRTYP="0" XPOS="820.001" NUMCO="16" POCOOR="0 0 0 0 144 0 144 0 144 0 144 0 144 87 144 87 144 87 144 87 0 87 0 87 0 87 0 87 0 0 0 0 " EXTRA="0" LOCALY="0" NUMDASH="0" LeftLine="0" PRFILE="" TEXTRA="0" SCALETYPE="1" TXTOUT="1" TXTFILL="Black" endArrowIndex="0" BEXTRA="0" PLINEJOIN="0" TXTSTP="-0.1" TXTULW="-0.1" TXTSCALEV="100" TXTSTRSH="100" >
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Group average." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" We can also define the distance between two clusters in such a way that all the pairwise distances contribute to the result. If we take the average of all the pairs then the method is called group average. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Ward's method." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" This method works like this: for each cluster we compute the sum of squared deviations from the cluster's centroid. Then we sum up all these sums and get a total error sum. At each step we merge the two clusters which minimize the increase of total error sum. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="McQuitty's method." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" In this method, after each merge, the distance between the new cluster and the old ones are computed based on the distances of the two clusters that were merged. In the example below, two clusters, A and B, were merge and formed a new cluster E. The distance D3 between E and another cluster C is defined to be D3= (size(A)×D1 + size(B)×D2)/(size(A) + size(B)). This method is also call WPGMA (Weighted Pair Group Method with Arithmetic Mean). " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Clustering using the Hamming distance and Ward's method." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" Let's now take a look at how the heatmap of the Hamming distances we introduced earlier looks like when we reorder it using Ward's algorithm. The most noticeable thing is the distinctive division of the map the due to nfs/proc and nfsd. Many things are clustered in expected ways: the ext2/ext3/ext4 family (lower left corner), the coda/smbfs/ncpfs network file systems, the jbd/jbd2 journaling services. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Dendrogram of the clustering using Hamming distance and Ward's method." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" If we look only at the dendrogram we can notice that this method divided the file systems in two big parts: complex disk-based systems including cluster file systems (which contain a disk-based part inside them), and everything else. We can also observe that most of the ancient file system category is contained almost completely in one big branch (fat–minix). Some unusual matches: 9p is situated quite far from the rest of the network file systems and tux3 ends up keeping company to the group of ancient file systems. In contrast, btrfs enjoys the neighborhood of xfs and gfs2 in the upper class of complex file systems. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Clustering using the Hamming distance and complete linkage." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" Unlike the previous method, the rearrangement using the clustering based on furthest neighbor strategy (also known as complete linkage) creates a heatmap with a nicely defined center. The kernel is formed by a group of ancient file system and a few memory-based file systems. In the lower left we can also notice a close-knit group formed by ext2/ext3/ext4, ocfs2 and reiserfs. As before, a few classic modules, jbd/jbd2 and coda/smbfs/ncpfs, are again together. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Dendrogram of the clustering using the Hamming distance and complete linkage." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" Here we can see that the big nice split from Ward's method is replaced by a more scatter division. The complex disk-based file systems are now split in two parts, ocfs2–ext3 and xfs–ubifs, the second of them being muddle by two flash-based file systems (jffs2 and ubifs). btrfs is again next to gfs2 and close to xfs but, surprise, also next to ntfs. Like before, tux3 is close to a bunch of ancient file systems. isofs, squashfs and cramfs, two read-only file systems are together from the start this time with romfs, the only other read-only file system, keeping a decent distance from them. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Clustering using the Hamming distance and group average." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" The group average method, usually used to identify bell-shaped clusters, generates a heatmap with a prominent off-center kernel. As in the previous case, this is made up of mostly by ancient file systems. Easily noticeable groups are again formed by the ext2/ext3/ext4, jbd/jbd2 and coda/smbfs/ncpfs. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Dendrogram of the clustering using the Hamming distance and group average." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" In this representation, the skew is also very visible. From a high-level perspective, we have a big cluster jbd–ubifs and a few small ones (ext4–ext3, gfs2–reiserfs and cifs–kafs) which are merged in the final merging steps with some file systems (nfs, btrfs, dlm, etc). The intuition behind this is that, as the file systems use more and more external symbols, they become more loosely connected. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Clustering using the Hamming distance and McQuitty's method." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" The heatmap in this case is somehow similar with the one from complete linkage. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Dendrogram of the clustering using the Hamming distance and McQuitty's method." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" If we ignore the skew induced by proc/nfsd/nfs and the fact that the complex disk-based file systems (xfs–reiserfs and ocfs2–ext3) are not sharing the same level, then the resulting tree is nicely split in similar things. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Following are a set of dendrograms using Canberra distance. In our case, this metric is equivalent with the number of different external symbols between two modules. After each dendrogram a reordered map of symbols is also plotted." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Phylogentic tree." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" Pars is a program that can construct an evolutionary tree which requires a minimum number of changes (maximum parsimony). The program is part of PHYLIP, a computational phylogenetics package created and maintained by Joseph Felsenstein. The input to Pars is number of species, each described using a string of characters. Usually each character is either "0" or "1" indicating the presence of absences of a certain feature but Pars also capable of dealing with up to 8 states plus "?" which indicates an unknown state. In our case we only need "0" and "1" and each position in the string encodes a certain external call.The result is the tree from upper right. It looks like a dendrogram but it is slightly different. This time the length of any vertical line is proportional with the number of changes between two states. We can see for example that msdos and vfat are both very close to the their parent while ext4 and ext3 are much farther apart. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Circular representations of the phylogentic tree." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" This are three alternative representations of the same tree. The size of the text is proportional with the depth. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="Circos." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Nimbus Sans L Bold" CSHX="5" CSHY="-5" CSTROKE="Black" />
<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH=" Circos is a visualization tool by Martin Krzywinski. The initial purpose was to provide a better representation of various genomic data but the program was successfully used to produce very nice graphical representations of other type of data.Let's now look at our plot. On the outer edge we have the file systems split in categories (from top to bottom: disk-based, optical mediums, flash-based, network-based, cluster-based, memory-based, ancient). The size is proportional with the number of external symbols. Colors indicate the type of external symbols. The green represents functions, red is data, orange are read-only data, and light yellow is uninitialized data (BSS). To give a sense of proportions, the external symbols exported by the Linux Kernel, vmlinux, are also depicted. It was compiled in the same configuration as the rest of the file systems. To give some numbers: it exports a total of 9310 external symbols out of which 8047 are functions, 621 are writable variables, 159 are read-only and 483 are BSS data. The gray area from file systems indicates the external symbols which are not satisfied by the kernel but by some other kernel module. This is noticeable for nfs, nfsd and also the users of jbd/jbd2: ext3, ext4, ocfs2." CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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<ITEXT CAB="5" CCOLOR="Black" CBASE="0" CSTW="-0.1" CSIZE="8" CULP="-0.1" CH="On the inner edge of vmlinux there is a plot that indicates the frequency which which each exported symbol is used by the file systems from right. One thing we noticed here is that variables are used pretty much with the same frequency as the functions.The set of boxes from the inner edge of the file systems represents the percentage of the external symbols which are unique to each file system. We can see that virtually all the external symbols used by proc are only used by it. But having unique external symbols is not a rare feature: with the exception of ancient file systems all the other categories have members with various degree of "uniqueness".The red arcs from inside depict the use-provide relationships between the file systems. As expected, the memory-based modules are the ones that are the main providers with proc and debufgs being the most popular one. We can also see that lockd is used by nfs and nfsd and also the relation between fat and vfat/msdos. A notable thing: there is no link between dlm and ocfs2/gfs2 because only the main kernel module was considered. " CSHADE2="100" CKERN="0" CSCALE="100" CSHADE="100" COUT="1" CSCALEV="100" CSTP="-0.1" CULW="-0.1" CSTYLE="0" CFONT="Century Schoolbook L Roman" CSHX="5" CSHY="-5" CSTROKE="Black" />
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