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Polynomial Fixed-Parameter Algorithms: A Case Study for Longest Path on Interval Graphs [article]

Archontia C. Giannopoulou, George B. Mertzios, Rolf Niedermeier
2021 arXiv   pre-print
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time.  ...  We show how to solve Longest Path on Interval Graphs, parameterized by vertex deletion number k to proper interval graphs, in O(k^9n) time.  ...  The authors wish to thank Jasper Slusallek for helpful discussions and for suggesting an improvement for the bounds given in Lemma 31.  ... 
arXiv:1506.01652v4 fatcat:ujcwctjlvraitisvtwc4fzitde

Polynomial fixed-parameter algorithms: A case study for longest path on interval graphs

Archontia C. Giannopoulou, George B. Mertzios, Rolf Niedermeier
2017 Theoretical Computer Science  
2017) 'Polynomial xed-parameter algorithms : a case study for longest path on interval graphs.', Theoretical computer science., 689 . pp. 67-95.  ...  We show how to solve Longest Path on Interval Graphs, parameterized by vertex deletion number k to proper interval graphs, in O(k 9 n) time.  ...  Then, using Algorithm 1 and the results of Sections 2 and 3, we conclude in Section 4.2 with our fixed-parameter algorithm for Longest Path on Interval Graphs, where the parameter k is the size of a minimum  ... 
doi:10.1016/j.tcs.2017.05.017 fatcat:hqpsz2b6tfhebdze455qkghuhm

Algorithms for Subnetwork Mining in Heterogeneous Networks [chapter]

Guillaume Fertin, Hafedh Mohamed Babou, Irena Rusu
2012 Lecture Notes in Computer Science  
We study the complexity of the problem, thus identifying polynomial, NP-complete and APX-hard cases. In order to solve the difficult cases, we propose a heuristic and a branch-and-bound algorithm.  ...  The sought pattern is a longest path in the directed graph whose vertex set induces a connected subgraph in the undirected graph.  ...  Further studies should either investigate the complexity of SkewGraM in terms of approximability (on specific graph classes) and fixed parameter algorithms, or inexact variants of the problem obtained,  ... 
doi:10.1007/978-3-642-30850-5_17 fatcat:2mhy7lq6lvbk5gfcvmpaup7so4

Smoothed Analysis of the 2-Opt Algorithm for the General TSP

Matthias Englert, Heiko Röglin, Berthold Vöcking
2016 ACM Transactions on Algorithms  
Smoothed Analysis of the 2-Opt Algorithm for the General TSP. ACM Trans. Algor. V, N, Article A (January YYYY), 15 pages.  ...  worst-case analysis in which the adversarial input is subject to a small amount of random noise.  ...  We study the length of the longest path in the state graph because this is the maximal number of local improvements the 2-Opt algorithm can make, regardless of the initial tour and regardless of which  ... 
doi:10.1145/2972953 fatcat:3dl7k46avne7dcaqkwy7buoc74

Algorithms and Complexity [chapter]

Peter Brucker, Sigrid Knust
2011 Complex Scheduling  
In Chapter 2, we extensively discuss various realistic communication models on which we conduct our study.  ...  of algorithms.  ...  Moreover, it is easy to compute the exact latency in polynomial time, since it only amounts to computing a longest path in a directed acyclic graph.  ... 
doi:10.1007/978-3-642-23929-8_2 fatcat:efxs6lrvbvfuvocbrelyqdpyma

The Maximum Binary Tree Problem

Karthekeyan Chandrasekaran, Elena Grigorescu, Gabriel Istrate, Shubhang Kulkarni, Young-San Lin, Minshen Zhu, Peter Sanders, Fabrizio Grandoni, Grzegorz Herman
2020 European Symposium on Algorithms  
MBT is a natural variant of the well-studied longest path problem, since both can be viewed as finding a maximum-sized tree of bounded degree in a given graph.  ...  The connection to longest path motivates the study of MBT in directed acyclic graphs (DAGs), since the longest path problem is solvable efficiently in DAGs.  ...  On the algorithmic side, we show that MBT in directed graphs is fixed-parameter tractable when parameterized by the solution size.  ... 
doi:10.4230/lipics.esa.2020.30 dblp:conf/esa/ChandrasekaranG20 fatcat:iia2l6tpgvdyxftcynq6l74u5y

Algorithms and Complexity of Range Clustering [article]

Dorit S. Hochbaum
2018 arXiv   pre-print
We propose a number of objective functions that employ the range of the clusters as part of the objective function. Several of the proposed objectives mimic objectives based on sums of similarities.  ...  Several of the problems we present could therefore be viable alternatives to existing clustering problems which are NP-hard, offering the advantage of efficient algorithms.  ...  Baumler for inspiring discussions that initiated the idea of range-clustering, and to Marjan Baghaie for her contributions to the writing of this paper and pointing out reference [17] .  ... 
arXiv:1805.04984v1 fatcat:6a2cziwiorfdlktwfoi4zk7l2u

Parallel Evolutionary Algorithms [chapter]

Dirk Sudholt
2015 Springer Handbook of Computational Intelligence  
Acknowledgments Part of this work was done while the author was a member of CERCIA, University of Birmingham, supported by EPSRC grant EP/D052785/1.  ...  In the case of evolutionary algorithms, an EA only needs to assign u as a predecessor of v on the shortest path in a lucky mutation in order to find a shortest path to v.  ...  In the single-source shortest paths problem (SSSP) one is looking for shortest paths from a source vertex to all other vertices of the graph.  ... 
doi:10.1007/978-3-662-43505-2_46 fatcat:kkhlsrruivcezdk5f7d62svcdu

Parameterized Algorithms in Bioinformatics: An Overview

Laurent Bulteau, Mathias Weller
2019 Algorithms  
This work surveys recent developments of parameterized algorithms and complexity for important NP-hard problems in bioinformatics.  ...  Bioinformatics regularly poses new challenges to algorithm engineers and theoretical computer scientists.  ...  Acknowledgments: The authors want to thank Fran Rosamond for suggesting the topic as well as everyone who helped collect interesting results for the manuscript, in particular Jesper Jansson, Steven Kelk  ... 
doi:10.3390/a12120256 fatcat:4dhjdnpibzh43iifgan2fu6bwa

Subexponential Parameterized Algorithms and Kernelization on Almost Chordal Graphs

Fedor V. Fomin, Petr A. Golovach, Peter Sanders, Grzegorz Herman, Fabrizio Grandoni
2020 European Symposium on Algorithms  
In particular, we construct a polynomial Turing kernel for Weighted Clique on Chordal-ke graphs.  ...  While various parameterized algorithms on graphs for many structural parameters like vertex cover or treewidth can be found in the literature, up to the Exponential Time Hypothesis (ETH), the existence  ...  Acknowledgements We thank Torstein Strømme, Daniel Lokshtanov, and Pranabendu Misra for fruitful discussions on the topic of this paper.  ... 
doi:10.4230/lipics.esa.2020.49 dblp:conf/esa/FominG20a fatcat:dh4jo3kb5rc3xgw7rqfted5doi

Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree [article]

Karthekeyan Chandrasekaran, Elena Grigorescu, Gabriel Istrate, Shubhang Kulkarni, Young-San Lin, Minshen Zhu
2021 arXiv   pre-print
We design a fixed-parameter algorithm with run-time w^O(w)n for the maximum-sized binary tree problem in undirected graphs when parameterized by treewidth w.  ...  In this work, we study parameterized algorithms for both longest heapable subsequence as well as maximum-sized binary tree. We show the following results: 1.  ...  Finally, we design a fixed-parameter algorithm for the maximum-sized binary tree problem in undirected graphs when parameterized by treewidth. We elaborate on our contributions now.  ... 
arXiv:2110.00495v2 fatcat:ztervkbxwfgw3gmhg5knjpqyqa

Computational Study on Bidimensionality Theory Based Algorithm for Longest Path Problem [chapter]

Chunhao Wang, Qian-Ping Gu
2011 Lecture Notes in Computer Science  
For example, the parameterized longest path problem is to determine, for a fixed integer k, whether G has a path of length k.  ...  Although the longest path problem can be solved in polynomial time for some classes of graphs such as interval graphs [42] , circular-arc graphs [10] , biconvex graphs [1] , and cocomparability graphs  ... 
doi:10.1007/978-3-642-25591-5_38 fatcat:622ghx3ekrc6jlfa6rsxip3rte

Parameterized Complexity and Approximation Algorithms

D. Marx
2007 Computer journal  
We discuss the different ways parameterized complexity can be extended to approximation algorithms, survey results of this type, and propose directions for future research.  ...  Approximation algorithms and parameterized complexity are usually considered to be two separate ways of dealing with hard algorithmic problems.  ...  I'm grateful to Martin Grohe and Magdalena Grüber for their comments on the manuscript.  ... 
doi:10.1093/comjnl/bxm048 fatcat:6yukdt7tvja3jf76zyuxfm536q

Polynomial-time algorithms for the Longest Induced Path and Induced Disjoint Paths problems on graphs of bounded mim-width [article]

Lars Jaffke, O-joung Kwon, Jan Arne Telle
2017 arXiv   pre-print
In particular, we give n^O(w)-time algorithms on graphs of mim-width at most w, when given a decomposition, for the following problems: Longest Induced Path, Induced Disjoint Paths and H-Induced Topological  ...  Our results imply that the following graph classes have polynomial-time algorithms for these three problems: Interval and Bi-Interval graphs, Circular Arc, Permutation and Circular Permutation graphs,  ...  Hence, designing an algorithm for a problem Π that runs in XP time parameterized by mim-width yields polynomial-time algorithms for Π on several interesting graph classes at once.  ... 
arXiv:1708.04536v2 fatcat:jy2vca4pmzc5rhkrnzhc4a5kju

Inapproximability of Orthogonal Compaction

Michael J. Bannister, David Eppstein, Joseph A. Simons
2012 Journal of Graph Algorithms and Applications  
We also provide a fixed-parameter-tractable algorithm for testing whether a drawing can be compacted to a small number of rows.  ...  We show that several problems of compacting orthogonal graph drawings to use the minimum number of rows, area, length of longest edge or total edge length cannot be approximated better than within a polynomial  ...  We also give a fixed-parameter tractable algorithm for finding compactions that use very small numbers of grid rows, for drawings in which such a compaction is possible.  ... 
doi:10.7155/jgaa.00263 fatcat:nnnk4r3fmzc5jhwcxzh2eyis4u
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