Edge separators of planar and outerplanar graphs with applications
Journal of Algorithms
Finding minimum-quotient cuts in planar graphs
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Parallel approximation schemes for problems on planar graphs
Acta Informatica
A survey of graph layout problems
ACM Computing Surveys (CSUR)
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 bisection problem asks for a partition of the n vertices of a graph into two sets of size at most ⌈n/2⌉, so that the number of edges connecting the two sets is minimised. A grid graph is a finite connected subgraph of the infinite two-dimensional grid. It is called solid if it has no holes. Papadimitriou and Sideri [8] gave an O(n5) time algorithm to solve the bisection problem on solid grid graphs. We propose a novel approach that exploits structural properties of optimal cuts within a dynamic program. We show that our new technique leads to an O(n4) time algorithm.