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

2021
*
arXiv
*
pre-print

We

arXiv:1506.01652v4
fatcat:ujcwctjlvraitisvtwc4fzitde
*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. ...##
###
Polynomial fixed-parameter algorithms: A case study for longest path on interval graphs

2017
*
Theoretical Computer Science
*

2017) '

doi:10.1016/j.tcs.2017.05.017
fatcat:hqpsz2b6tfhebdze455qkghuhm
*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 ...##
###
Algorithms for Subnetwork Mining in Heterogeneous Networks
[chapter]

2012
*
Lecture Notes in Computer Science
*

We

doi:10.1007/978-3-642-30850-5_17
fatcat:2mhy7lq6lvbk5gfcvmpaup7so4
*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, ...##
###
Smoothed Analysis of the 2-Opt Algorithm for the General TSP

2016
*
ACM Transactions on Algorithms
*

Smoothed Analysis of the 2-Opt

doi:10.1145/2972953
fatcat:3dl7k46avne7dcaqkwy7buoc74
*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 ...##
###
Algorithms and Complexity
[chapter]

2011
*
Complex Scheduling
*

In Chapter 2, we extensively discuss various realistic communication models

doi:10.1007/978-3-642-23929-8_2
fatcat:efxs6lrvbvfuvocbrelyqdpyma
*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*. ...##
###
The Maximum Binary Tree Problem

2020
*
European Symposium on Algorithms
*

MBT is

doi:10.4230/lipics.esa.2020.30
dblp:conf/esa/ChandrasekaranG20
fatcat:iia2l6tpgvdyxftcynq6l74u5y
*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. ...##
###
Algorithms and Complexity of Range Clustering
[article]

2018
*
arXiv
*
pre-print

We propose

arXiv:1805.04984v1
fatcat:6a2cziwiorfdlktwfoi4zk7l2u
*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] . ...##
###
Parallel Evolutionary Algorithms
[chapter]

2015
*
Springer Handbook of Computational Intelligence
*

Acknowledgments Part of this work was done while the author was

doi:10.1007/978-3-662-43505-2_46
fatcat:kkhlsrruivcezdk5f7d62svcdu
*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*. ...##
###
Parameterized Algorithms in Bioinformatics: An Overview

2019
*
Algorithms
*

This work surveys recent developments of

doi:10.3390/a12120256
fatcat:4dhjdnpibzh43iifgan2fu6bwa
*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 ...##
###
Subexponential Parameterized Algorithms and Kernelization on Almost Chordal Graphs

2020
*
European Symposium on Algorithms
*

In particular, we construct

doi:10.4230/lipics.esa.2020.49
dblp:conf/esa/FominG20a
fatcat:dh4jo3kb5rc3xgw7rqfted5doi
*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. ...##
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Fixed-Parameter Algorithms for Longest Heapable Subsequence and Maximum Binary Tree
[article]

2021
*
arXiv
*
pre-print

We design

arXiv:2110.00495v2
fatcat:ztervkbxwfgw3gmhg5knjpqyqa
*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. ...##
###
Computational Study on Bidimensionality Theory Based Algorithm for Longest Path Problem
[chapter]

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*...

##
###
Parameterized Complexity and Approximation Algorithms

2007
*
Computer journal
*

We discuss the different ways

doi:10.1093/comjnl/bxm048
fatcat:6yukdt7tvja3jf76zyuxfm536q
*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. ...##
###
Polynomial-time algorithms for the Longest Induced Path and Induced Disjoint Paths problems on graphs of bounded mim-width
[article]

2017
*
arXiv
*
pre-print

In particular, we give n^O(w)-time

arXiv:1708.04536v2
fatcat:jy2vca4pmzc5rhkrnzhc4a5kju
*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. ...##
###
Inapproximability of Orthogonal Compaction

2012
*
Journal of Graph Algorithms and Applications
*

We also provide

doi:10.7155/jgaa.00263
fatcat:nnnk4r3fmzc5jhwcxzh2eyis4u
*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. ...
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