Parallel approximation schemes for problems on planar graphs
Acta Informatica
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On partitioning a graph: a theoretical and empirical study.
On partitioning a graph: a theoretical and empirical study.
Optimal hierarchical decompositions for congestion minimization in networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Simple cuts are fast and good: optimum right-angled cuts in solid grids
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Fast balanced partitioning is hard even on grids and trees
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Corner cuts are close to optimal: From solid grids to polygons and back
Discrete Applied Mathematics
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The graph bisection problem asks to partition the n vertices of a graph into two sets of equal size so that the number of edges across the cut is minimum. We study finite, connected subgraphs of the infinite two-dimensional grid that do not have holes. Since bisection is an intricate problem, our interest is in the tradeoff between runtime and solution quality that we get by limiting ourselves to a special type of cut, namely cuts with at most one bend each (corner cuts). We prove that optimum corner cuts get us arbitrarily close to equal sized parts, and that this limitation makes us lose only a constant factor in the quality of the solution. We obtain our result by a thorough study of cuts in polygons and the effect of limiting these to corner cuts.