Abstract
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 \(\mathcal{O}(n^5)\) 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 \(\mathcal{O}(n^4)\) time algorithm.
We gratefully acknowledge discussions with Peter Arbenz, and the support of this work through the Swiss National Science Foundation under Grant No. 200021_125201/1.
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Feldmann, A.E., Widmayer, P. (2011). An \(\mathcal{O}(n^4)\) Time Algorithm to Compute the Bisection Width of Solid Grid Graphs. In: Demetrescu, C., Halldórsson, M.M. (eds) Algorithms – ESA 2011. ESA 2011. Lecture Notes in Computer Science, vol 6942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23719-5_13
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DOI: https://doi.org/10.1007/978-3-642-23719-5_13
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