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A longest path between two given vertices s and t in a weighted graph G is the same thing as a shortest path in a graph −G derived from G by changing every weight to its negation. Therefore, if shortest paths can be found in −G, then longest paths can also be found in G. [4]
naraview – A game which you need to find a connection between two articles in Wikipedia. Six Degrees – The new version of the Facebook application originally built by Karl Bunyan. Facebook revised policy on caching data Archived 2014-12-09 at the Wayback Machine – Facebook's revised policy removing the 24-hour limit on caching of user data.
The items separated by the longest minimal chains in the encyclopedia (especially where these are more than four links long). The shortest known chain between the two items should be specified. Generalisation over time, where possible, seems to produce the shortest chains. Failing this, try generalisation over space to reduce chain length.
Milgram's experiment developed out of a desire to learn more about the probability that two randomly selected people would know each other. [6] This is one way of looking at the small world problem. An alternative view of the problem is to imagine the population as a social network and attempt to find the average path length between any two ...
Average path length is one of the three most robust measures of network topology, along with its clustering coefficient and its degree distribution.Some examples are: the average number of clicks which will lead you from one website to another, or the number of people you will have to communicate through, on an average, to contact a complete stranger.
Dijkstra's algorithm can be used to find the shortest path between two articles in Wikipedia. There will be two articles connected by a shortest path which is longer than any other shortest path between any of the other articles in Wikipedia. 82.136.254.117 wondered what those two articles are. I think this is a non-trivial problem.
Conversely, if H has an induced path or cycle of length k, any maximal set of nonadjacent vertices in G from this path or cycle forms an independent set in G of size at least k/3. Thus, the size of the maximum independent set in G is within a constant factor of the size of the longest induced path and the longest induced cycle in H.
A more efficient method would never repeat the same distance calculation. For example, the Levenshtein distance of all possible suffixes might be stored in an array , where [] [] is the distance between the last characters of string s and the last characters of string t. The table is easy to construct one row at a time starting with row 0.
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