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Given an undirected cyclic planar graph G(V,E) with vertex weights W(V), a fixed plane embedding E(G) and two nodes s and t, I need to find a partitioning of G that divides it into two connected components S(G) and T(G) with s being in S(G) and t being in T(G). Vertices s and t both belong to the external face in the embedding E(G).

I wish to have the partitions well balanced - they should have nearly equal sums of vertex weights.

Any ideas for a good algorithm please?

Tomas
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Isolin
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  • I have a similar problem (https://stackoverflow.com/questions/50499117/partition-a-graph-around-two-vertices). Were you able to find a solution? – Shirish Kumar May 24 '18 at 17:14
  • No. As far as I remember, used a simple heuristics which did not perform very well. I abandoned the problem some time later unfinished. – Isolin May 31 '18 at 22:40

2 Answers2

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Compute a Minimum Spanning Tree and use in conjunction with an AVL Tree balancing properties?

James
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  • The spanning tree will not be binary and the usage of AVL for balancing by vertex weights is unclear to me. Do you have any details on your idea? Yet, I'm rather confused. – Isolin Feb 06 '11 at 18:54
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It is some sort of balanced cut problem which is NP Complete in general and has logarithmic factor approximation algorithms. If im correct then it is weakly NP hard in planar graphs with 2 approx algorithm by naveen garg.(chk it on google)

singhsumit
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