
An optimal FPT algorithm parametrized by treewidth for WeightedMaxBisection given a tree decomposition as advice assuming SETH and the hardness of MinConv
The weighted maximal bisection problem is, given an edge weighted graph,...
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Current Algorithms for Detecting Subgraphs of Bounded Treewidth are Probably Optimal
The Subgraph Isomorphism problem is of considerable importance in comput...
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Solving InfiniteDomain CSPs Using the Patchwork Property
The constraint satisfaction problem (CSP) has important applications in ...
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Degrees and Gaps: Tight Complexity Results of General Factor Problems Parameterized by Treewidth and Cutwidth
For the General Factor problem we are given an undirected graph G and fo...
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Nearly ETHTight Algorithms for Planar Steiner Tree with Terminals on Few Faces
The Planar Steiner Tree problem is one of the most fundamental NPcomple...
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Waypoint Routing on Bounded Treewidth Graphs
In the Waypoint Routing Problem one is given an undirected capacitated a...
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Counting list homomorphisms from graphs of bounded treewidth: tight complexity bounds
The goal of this work is to give precise bounds on the counting complexi...
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An optimal algorithm for Bisection for boundedtreewidth graphs
The maximum/minimum bisection problems are, given an edgeweighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is maximized/minimized. Although these two problems are known to be NPhard, there is an efficient algorithm for boundedtreewidth graphs. In particular, Jansen et al. (SIAM J. Comput. 2005) gave an O(2^tn^3)time algorithm when given a tree decomposition of width t of the input graph, where n is the number of vertices of the input graph. Eiben et al. (ESA 2019) improved the running time to O(8^tt^5n^2log n). Moreover, they showed that there is no O(n^2ε)time algorithm for trees under some reasonable complexity assumption. In this paper, we show an O(2^t(tn)^2)time algorithm for both problems, which is asymptotically tight to their conditional lower bound. We also show that the exponential dependency of the treewidth is asymptotically optimal under the Strong Exponential Time Hypothesis. Moreover, we discuss the (in)tractability of both problems with respect to special graph classes.
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