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README.md

README

Reference

Letsios, M., Balalau, O. D., Danisch, M., Orsini, E., & Sozio, M..
Finding heaviest k-subgraphs and events in social media.
In Data Mining Workshops (ICDMW), 2016 IEEE 16th International Conference on (pp. 113-120). IEEE.

Info

bb_dks.c finds the heaviest subgraph of k nodes in a weighted graph (that is a subgraph containing exactly k nodes such that the sum of the weight on its edges is maximized). The result is exact. It scales to real-world networks containing several billions of edges and for k up to 10, 20 or more depending on the structure of the graph.

bb_dks_approx.c solves an approximated version of the problem. It finds a subgraph of k nodes or less such that the sum of the weight on its edges is at least 1/alpha times the one of the heaviest subgraph of k nodes.

The algorithms are both based on branch and bound, the branching phase is based on deciding whether to include an edge in the subgraph or not, edges are examined in non-increasing order of weight.

wcore.c computes an ordering of the vertices according to the weighted kcore (or weighted degeneracy ordering) and compute the weight of the subgraphs induced by all prefixes. It can be used to find a heavy subgraph of any k, it does not have any fixed parameter approximation guaranty but is faster than the two algorithms based on branch and bound.

improvegreedy.c and improvestochastic.c are local search algorithms that improve a solution by switching a node inside the subgraph of size k and a node outside the subgraph such that the weight of the subgraph increases. It stops when the solution becomes a stable local optimum with respect to this switch operation.
improvegreedy.c picks the best switch everytime, while improvestochastic.c picks a random switch that will improve the solution.

A stackexchange question on the topic: http://cstheory.stackexchange.com/questions/20221/find-the-densest-subgraph-of-size-k

A paper on the subject: https://papers-gamma.link/paper/8

To compile

gcc bb_dks.c -o bb_dks -O3
gcc bb_dks_approx.c -o bb_dks_approx -O3
gcc wcore.c -o wcore -O3
gcc improvegreedy.c -o improvegreedy -O3
gcc improvestochastic.c -o improvestochastic -O3

To execute

./bb_dks k net.txt
./bb_dks_approx k alpha net.txt

  • k is an integer
  • alpha should be greater than one.
  • net.txt should contain the weighted graph "nodeID1 nodeID2 weight". It is better if the nodeIDs are from 0 to n-1. NO SELF-LOOP and ONLY SIMPLE EDGES!

It will print:

  • some info
  • total_weight
  • the k nodes

./wcore net.txt res.txt

Will print in res.txt "size nodeID weight" on each line, where weight is the sum of the weights of the subgraph induced on all previous nodes.

./improvegreedy net.txt init.txt res.txt
./improvestochastic net.txt init.txt res.txt

init.txt should contain the initial subgraph in the format: "weight k nodeID1 nodeID2 nodeID3 ... nodeIDk"
Will print in res.txt "weight k nodeID1 nodeID2 nodeID3 ... nodeIDk", where weight is the sum of the weights of the subgraph induced on the k nodes.

Initial contributors

Maximilien Danisch
The branch and bound code is adapted from the java version of Manthos Letsios
Technical consultants: Oana Balalau, Emmanuel Orsini and Mauro Sozio
September 2016
http://bit.ly/danisch
maximilien.danisch@gmail.com

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C code to compute a Heaviest k-Subgraph or an approximation

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