Abstract
The Multicut problem is defined as follows: given a graph G and a collection of pairs of distinct vertices (s i; t i) of G, find a small- est set of edges of G whose removal disconnects each s i from the corre- sponding t i. Our main result is a polynomial-time approximation scheme for Multicut in unweighted graphs with bounded degree and bounded tree-width: for any ∈ > 0, we presented a polynomial-time algorithm with performance ratio at most 1 + ∈. In the particular case when the input is a bounded-degree tree, we have a linear-time implementation of the algorithm. We also provided some hardness results. We proved that Multicut is still NP-hard for binary trees and that, unless P = NP, no polynomial-time approximation scheme exists if we drop any of the the three conditions: unweighted, bounded-degree, bounded-tree-width. Some of these results extend to the vertex version of Multicut.
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Research supported in part by NSF grant CCR-9319106.
Research partially supported by NSF grant CCR-9319106 and by FAPESP (Proc. 96/04505-2).
Research supported in part by ProNEx (MCT/FINEP) (Proj. 107/97) and FAPESP (Proc. 96/12111-4).
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Călinescu, G., Fernandes, C.G., Reed, B. (1998). Multicuts in Unweighted Graphs with Bounded Degree and Bounded Tree-Width. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-69346-7_11
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