A nearly-linear time algorithm for linear programs with small treewidth: a multiscale representation of robust central path
Sally Dong, Yin Tat Lee, Guanghao Ye
Abstract
Arising from structural graph theory, treewidth has become a focus of study in fixed-parameter tractable algorithms. Many NP-hard problems are known to be solvable in O(n · 2O(τ)) time, where τ is the treewidth of the input graph. Analogously, many problems in P should be solvable in O(n · τO(1)) time; however, due to the lack of appropriate tools, only a few such results are currently known. In our paper, we show this holds for linear programs: Given a linear program of the form minAx=b,ℓ ≤ x≤ u c⊤ x whose dual graph GA has treewidth τ, and a corresponding width-τ tree decomposition, we show how to solve it in time
Topics & Concepts
TreewidthTree decompositionTime complexityGraphMathematicsCombinatoricsPartial k-treePath (computing)Tree-depthRepresentation (politics)AlgorithmDiscrete mathematicsComputer sciencePathwidthLine graphPolitical scienceLawPoliticsProgramming languageAdvanced Graph Theory ResearchComplexity and Algorithms in GraphsVLSI and FPGA Design Techniques