What are sufficient file information for file hashing? - algorithm

Question

Since making a hash of a complete binary file would be far too heavy to compute in a reasonably fast time:
What are sufficient file information for hashing a file? The following lists what properties the resulting hashing should ideally have:
collision-free in respect to other files in the directory
fast
catch all file changes
As a rule of thumb, the less information we can use to create enough entropy, the better. Since the speed of retrieval for specific information may depend largely on the given environment (OS, file-IO of the language, IO of the used library, etc.), it should be disregarded here.
(This is my first attempt at a community wiki. My reason for making it one is that the information asked here is very generic but (hopefully) informative. I also would like this question to be marked as a community wiki, so it can be improved where fit. )

Answer 1

General Overview
Our goal here is to track as much differences between two file states while not using redundant data. Thus each informational source must be a disjointed subset of the information of the files state.
The following items represent sources of information about a file:
the name of the file
the directory-path relative to the specified document-root (aka absolute from document-root)
the files permissions
the files owner (user/group)
the last change time
the size of the file
the hostname of the machine the file resides on
the actual saved binary data
Per Item Considerations
Name of File
The name of the file is part of its absolute filesystem's path (the last bit) and as #La-comadreja said, it is unique in that no two files on a system can have the same absolute path. Using the File's name in combination with the rest of its absolute path (see directory-path for more information) is highly encouraged to avoid hash collisions with other files.
Directory-Path
While the files absolute path will be perfectly unique, it should be noted that in certain circumstances hashing the absolute path may be inappropriate. For instance, comparing the hashes of two files on different machines will most likely fail when both files do not have the identical absolute path on both machines. This becomes even more problematic on machines with different OS's and/or architectures. It is therefore encouraged to specify a document-root and resolve an absolute path from there.
Permissions
If you want to track changes to a files permissions, the tests below indicate that you would need to incoporate them into your hash directly as they do not change any other information about the file (most notably the timestamp). Note however that permissions are handled quite differently on different machines, so caution must be exercised here (for instance to use a canonical permission translation scheme).
Ownership
Ownership, just as permissions, is handled very differently across architectures and filesystems. A change of ownership does not change other information (as indicated by the tests below).
timestamp
The timestamp of a file is also something that is not unifiedly implemented across all (or at least the most common) systems. First of all, there are different timestamps on different filesystems we could be looking at: creation date, modified date, access date, etc. For our purpose the modified date is most suitable, as it is supported by most of the available filesystems [1] and holds the exact information we need: the last change to a file. However comparing files across different OS's may pose a problem, as Windows and Unix handle timestamps (in general) differently (see here [2] for a detailed article about the problem). Note that the modification date of a file changes whenever a file has been edited (disregarding edge cases), so timestamp indicates changes in file size (note that the opposite does not hold true, see file-size).
File size
The file size in bytes is an extremely good indication whether a file has been edited (except for permissions, ownership and name changes), as each edit would change the files content, thus changing its size. However this does not hold true if additions to a file are exactly as big as deletions. Thus the files timestamp may be a better indicator. Also, calculating a files binary size may be quite computation intensive.
Hostname
If one wants to compare files across multiple hosts and regard identical files on different hosts as different, then the hostname of the machine (or another suitable unique identifier for the host) should be included in the hash.
Binary Data
The binary data of the file has, of course, all necessary information to check if a file was changed. However, it is also too resource intensive to be of any practicability. It i highly discouraged to use this information.
Suggestions
The following sources should be used to compare files:
the name of the file
the directory path
the timestamp (see above for problems)
The following extra sources can be used to track more information:
permissions (see above)
ownership (see above)
hostname (when comparing across different machines)
The following sources of information should be disregarded:
file size
binary data
Tests
I did some tests on Debian checking whether changing one information would change another. Most interestingly rename, permission change, owner change did not affect a timestamp change or filesize change. (Note that these tests are currently only tested on Debian Linux. Other OS's will likely behave differently.)
$ ls -l
-rw-r--r-- 1 alex alex 30 Apr 26 11:04 bar
-rw-r--r-- 1 alex alex 0 Apr 26 11:03 baz
-rw-r--r-- 1 alex alex 14 Apr 26 11:04 foo
$ mv baz baz2
$ ls -l
-rw-r--r-- 1 alex alex 30 Apr 26 11:04 bar
-rw-r--r-- 1 alex alex 0 Apr 26 11:03 baz2
-rw-r--r-- 1 alex alex 14 Apr 26 11:04 foo
$ chmod 777 foo
$ ls -l
-rw-r--r-- 1 alex alex 30 Apr 26 11:04 bar
-rw-r--r-- 1 alex alex 0 Apr 26 11:03 baz2
-rwxrwxrwx 1 alex alex 14 Apr 26 11:04 foo
$ mv baz2 baz
$ echo "Another string" >> bar
$ ls -l
-rw-r--r-- 1 alex alex 45 Apr 26 11:17 bar
-rw-r--r-- 1 alex alex 0 Apr 26 11:03 baz
-rwxrwxrwx 1 alex alex 14 Apr 26 11:04 foo
$ sudo chown root baz
$ ls -l
-rw-r--r-- 1 alex alex 45 Apr 26 11:17 bar
-rw-r--r-- 1 root alex 0 Apr 26 11:03 baz
-rwxrwxrwx 1 alex alex 14 Apr 26 11:04 foo

Answer 2

Assuming all the files are on the same machine, directory path and file name should produce a unique combination because two files in the same directory cannot have the same name. Directory path, filename and timestamp of last change should capture each change.
If the files are on different machines, the machine name should be included in the directory path.