Abstract
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.
Original language | English |
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Pages (from-to) | 86-91 |
Number of pages | 6 |
Journal | Discrete Applied Mathematics |
Volume | 164 |
Issue number | PART 1 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Keywords
- Exchange algorithm
- Room-partitioning
- Two-person games