Turbocharging Treewidth Heuristics
A widely used class of algorithms for computing tree decompositions of graphs are heuristics that compute an elimination order, i.e., a permutation of the vertex set. In this paper, we propose to turbocharge these heuristics. For a target treewidth k, suppose the heuristic has already computed a partial elimination order of width at most k, but extending it by one more vertex exceeds the target width k. At this moment of regret, we solve a subproblem which is to recompute the last c positions of the partial elimination order such that it can be extended without exceeding width k. We show that this subproblem is fixed-parameter tractable when parameterized by k and c, but it is para-NP-hard and W[1]-hard when parameterized by only k or c, respectively. Our experimental evaluation of the FPT algorithm shows that we can trade a reasonable increase of the running time for quality of the solution.
tree decomposition
heuristic
fixed-parameter tractability
local search
13:1-13:13
Regular Paper
Serge
Gaspers
Serge Gaspers
Joachim
Gudmundsson
Joachim Gudmundsson
Mitchell
Jones
Mitchell Jones
Julián
Mestre
Julián Mestre
Stefan
Rümmele
Stefan Rümmele
10.4230/LIPIcs.IPEC.2016.13
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