SIAM Journal on Computing
Parallel approximation schemes for problems on planar graphs
Acta Informatica
The bisection width of grid graphs
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
A survey of graph layout problems
ACM Computing Surveys (CSUR)
A Polylogarithmic Approximation of the Minimum Bisection
SIAM Journal on Computing
On partitioning a graph: a theoretical and empirical study.
On partitioning a graph: a theoretical and empirical study.
Theory of Computing Systems
Partitioning graphs into balanced components
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
An O(n4) time algorithm to compute the bisection width of solid grid graphs
ESA'11 Proceedings of the 19th European conference on Algorithms
Restricted cuts for bisections in solid grids: a proof via polygons
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
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We consider the problem of bisecting a graph, i.e. cutting it into two equally sized parts while minimising the number of cut edges. In its most general form the problem is known to be NP-hard. Several papers study the complexity of the problem when restricting the set of considered graphs. We attempt to study the effects of restricting the allowed cuts. We present an algorithm that bisects a solid grid, i.e. a connected subgraph of the infinite two-dimensional grid without holes, using only cuts that correspond to a straight line or a right angled corner. It was shown in [13] that an optimal bisection for solid grids with n vertices can be computed in O(n5) time. Restricting the cuts in the proposed way we are able to improve the running time to O(n4). We prove that these restricted cuts still yield good solutions to the original problem: The best restricted cut is a bicriteria approximation to an optimal bisection w.r.t. both the differences in the sizes of the partitions and the number of edges that are cut.