How Good is Recursive Bisection?
SIAM Journal on Scientific Computing
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
Mathematics of Operations Research
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 study the solution quality for min-cut problems on graphs when restricting the shapes of the allowed cuts. In particular we are interested in min-cut problems with additional size constraints on the parts being cut out from the graph. Such problems include the bisection problem, the separator problem, or the sparsest cut problem. We therefore aim at cutting out a given number m of vertices from a graph using as few edges as possible. We consider this problem on solid grid graphs, which are finite, connected subgraphs of the infinite two-dimensional grid that do not have holes. Our interest is in the tradeoff between the simplicity of the cut shapes and their solution quality: we study corner cuts in which each cut has at most one right-angled bend. We prove that optimum corner cuts get us arbitrarily close to a cut-out part of size m, 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.