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I have a graph G=(V,E) that both edges and nodes have weights. I want to partition this graph to create equal sized partitions. The definition of the size of partition is sum(vi)-sum(ej) where vi is a node inside that partition and ej is an edge between two nodes in that partition. In my problem the graph is very dense (almost complete). Is there any approximation algorithm for that?

This is somehow similar to the problem in bin packing with overlapping objects where bins have the same size. Weight of nodes are their size and weight of Edges show how much two object can overlap.

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Masood_mj
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  • Making all weights negative and then adding the weight of nodes as an edge to the same node, the problem will be to create partitions that have the same sum(ei) – Masood_mj Jul 25 '12 at 20:04
  • What happens to edges between two nodes in different partitions? Also, do you want a bipartition or a partition of any size? Edit: never mind, from looking at the other question you want a partition of any order and the edges between partitions don't matter. – jclancy Jul 31 '12 at 13:47

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I think if you use METIS program solved problem. you can download this program of this link http://glaros.dtc.umn.edu/gkhome/views/metis it has a good documentation and very fast program.

mohammadjavadkh
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