Improved fixed parameter tractable algorithms for two “edge” problems: MAXCUT and MAXDAG

Raman, Venkatesh; Saurabh, Saket

doi:10.1016/j.ipl.2007.05.014

Cited by 19 publications

(14 citation statements)

References 15 publications

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“…They explicitly asked whether the kernel size can be improved to O(k) vertices, and whether the run time can be improved to 2 O(k) · n O (1) . Here, we answer their questions in the affirmative by using Theorem 3 and then applying an O * (2 n )-time algorithm by Raman and Saurabh [35,Thm. 2] to our kernel with O(k) vertices.…”

Section: Theorem 3 Let π Be Any Strongly λ-Extendible Property Of (Pomentioning

confidence: 96%

Linear Kernels and Linear-Time Algorithms for Finding Large Cuts

Etscheid

Mnich

2017

Algorithmica

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The maximum cut problem in graphs and its generalizations are fundamental combinatorial problems. Several of these cut problems were recently shown to be fixed-parameter tractable and admit polynomial kernels when parameterized above the tight lower bound measured by the size and order of the graph. In this paper we continue this line of research and considerably improve several of those results: Dedicated to the 60th birthday of Gregory Gutin. All presented kernels can be computed in time O(km). Supported by ERC Starting Grant 306465 (BeyondWorstCase

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Section: Theorem 3 Let π Be Any Strongly λ-Extendible Property Of (Pomentioning

confidence: 96%

Linear Kernels and Linear-Time Algorithms for Finding Large Cuts

Etscheid

Mnich

2017

Algorithmica

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“…First, an extended version of the search tree algorithm showing fixed-parameter tractability with respect to the Kemeny score [3]. Second, a dynamic programming algorithm running in O(2 m · nm 2 ) time for m candidates and n votes [3,14]. Third, the integer linear program [5, Linear Program 3] which was the fastest exact algorithm in previous experimental studies [5,15].…”

Section: Resultsmentioning

confidence: 99%

Partial Kernelization for Rank Aggregation: Theory and Experiments

Betzler

Bredereck

Niedermeier

2010

Parameterized and Exact Computation

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Abstract. RANK AGGREGATION is important in many areas ranging from web search over databases to bioinformatics. The underlying decision problem KE-MENY SCORE is NP-complete even in case of four input rankings to be aggregated into a "median ranking". We study efficient polynomial-time data reduction rules that allow us to find optimal median rankings. On the theoretical side, we improve a result for a "partial problem kernel" from quadratic to linear size. On the practical side, we provide encouraging experimental results with data based on web search and sport competitions, e.g., computing optimal median rankings for real-world instances with more than 100 candidates within milliseconds.

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“…This is one of the 21 problems shown to be NP-hard by Karp's seminal work [12]. To overcome this intractability, numerous researches have been done from the viewpoints of approximation algorithms [8,13,11,25], exponential-time exact algorithms [7,26], and fixed-parameter algorithms [3,16,17,22]. There are several graph classes for which the Max-Cut problem admits polynomial time algorithms [1,9].…”

Section: Introductionmentioning

confidence: 99%

An Improved Fixed-Parameter Algorithm for Max-Cut Parameterized by Crossing Number

Kobayashi

Miyazaki

et al. 2019

Lecture Notes in Computer Science

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The Max-Cut problem is known to be NP-hard on general graphs, while it can be solved in polynomial time on planar graphs. In this paper, we present a fixed-parameter tractable algorithm for the problem on "almost" planar graphs: Given an n-vertex graph and its drawing with k crossings, our algorithm runs in time O(2 k (n + k) 3/2 log(n + k)). Previously, Dahn, Kriege and Mutzel (IWOCA 2018) obtained an algorithm that, given an n-vertex graph and its 1-planar drawing with k crossings, runs in time O(3 k n 3/2 log n). Our result simultaneously improves the running time and removes the 1-planarity restriction.

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Improved fixed parameter tractable algorithms for two “edge” problems: MAXCUT and MAXDAG

Cited by 19 publications

References 15 publications

Linear Kernels and Linear-Time Algorithms for Finding Large Cuts

Linear Kernels and Linear-Time Algorithms for Finding Large Cuts

Partial Kernelization for Rank Aggregation: Theory and Experiments

An Improved Fixed-Parameter Algorithm for Max-Cut Parameterized by Crossing Number

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