Note: MAX-CUT and MAX-BISECTION are NP-hard on unit disk graphs
Theoretical Computer Science
Polynomial constraint satisfaction problems, graph bisection, and the Ising partition function
ACM Transactions on Algorithms (TALG)
Approximation algorithms for geometric intersection graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Local search: Is brute-force avoidable?
Journal of Computer and System Sciences
Linear-programming design and analysis of fast algorithms for Max 2-CSP
Discrete Optimization
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The max-bisection and min-bisection problems are to find a partition of the vertices of a graph into two equal size subsets that, respectively, maximizes or minimizes the number of edges with endpoints in both subsets.We design the first polynomial time approximation scheme for the max-bisection problem on arbitrary planar graphs solving a long-standing open problem. The method of solution involves designing exact polynomial time algorithms for computing optimal partitions of bounded treewidth graphs, in particular max- and min-bisection, which could be of independent interest.Using a similar method we design also the first polynomial time approximation scheme for max-bisection on unit disk graphs (which could also be easily extended to other geometrically defined graphs).