Exponentiality of the exchange algorithm for finding another room-partitioning: 1

Let T be a triangulated surface given by the list of vertex-triples of its triangles, called rooms. A room-partitioning for T is a subset R of the rooms such that each vertex of T is in exactly one room in R. Given a room-partitioning R for T, the exchange algorithm walks from room to room until it finds a second different room-partitioning R'. In fact, this algorithm generalizes the Lemke-Howson algorithm for finding a Nash equilibrium for two-person games. In this paper, we show that the running time of the exchange algorithm is not polynomial relative to the number of rooms, by constructing a sequence of (planar) instances, in which the algorithm walks from room to room an exponential number of times. We also show a similar result for the problem of finding a second perfect matching in Eulerian graphs. (C) 2012 Elsevier B.V. All rights reserved.

Published in:
Discrete Applied Mathematics, 164, 86-91
Presented at:
1st International Symposium on Combinatorial Optimization (ISCO), Hammamet, TUNISIA, MAR 24-26, 2010
Amsterdam, Elsevier Science Bv

 Record created 2014-05-02, last modified 2018-09-13

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