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A Tight Analysis of the Maximal Matching Heuristic
[chapter]

2005
*
Lecture Notes in Computer Science
*

These bounds are obtained through

doi:10.1007/11533719_71
fatcat:jch3ymqmgjaplhgfzjxwnaxba4
*a*careful*analysis**of**the**tight*examples. Chercheur qualifié du F.N.R.S. Corresponding author. ... This algorithm is*a*well-known 2-approximation to three classical NP-hard optimization problems: MINIMUM VERTEX COVER, MINIMUM*MAXIMAL**MATCHING*and MINIMUM EDGE DOMINATING SET. ...*The*above theorem gives*a**tight*upper bound on*the*approximation ratio*of**the**maximal**matching**heuristic*to*the*minimum vertex cover problem in graphs*of*n vertices and m edges, in*the*form*of**a*discrete ...##
###
Combinatorial Dominance Guarantees for Heuristic Algorithms

2007
*
Discrete Mathematics & Theoretical Computer Science
*

In particular, we show that

doi:10.46298/dmtcs.3537
fatcat:rbxjfc7oofhj7ac47hbd2jt6de
*the*well-known $\textit{*maximal**matching*}$*heuristic**of*$\textit{Vertex Cover}$ provides an excellent dominance bound. ... We introduce new general*analysis*techniques which apply to*a*wide range*of*problems and*heuristics*for this measure. ... One example is*the*well-known*maximal**matching**heuristic*, which takes both endpoints*of*all edges in any*maximal**matching*. ...##
###
Improved approximation bounds for edge dominating set in dense graphs

2009
*
Theoretical Computer Science
*

This algorithm provides

doi:10.1016/j.tcs.2008.12.036
fatcat:6saeb2h3pbaurcwm2w3fpknri4
*a*2-approximation to*the*minimum edge dominating set and minimum*maximal**matching*problems. ... We analyze*the*simple greedy algorithm that iteratively removes*the*endpoints*of**a*maximum-degree edge in*a*graph, where*the*degree*of*an edge is*the*sum*of**the*degrees*of*its endpoints. ... Acknowledgments*The*authors wish to thank Martine Labbé, with whom this research was initiated, and Hadrien Mélot, author*of**the*GraPHedron software [16] , which was used to formulate*the*initial conjectures ...##
###
Improved Approximation Bounds for Edge Dominating Set in Dense Graphs
[chapter]

2007
*
Lecture Notes in Computer Science
*

This algorithm provides

doi:10.1007/11970125_9
fatcat:n4kvqo4oerfyday24dappnllee
*a*2-approximation to*the*minimum edge dominating set and minimum*maximal**matching*problems. ... We analyze*the*simple greedy algorithm that iteratively removes*the*endpoints*of**a*maximum-degree edge in*a*graph, where*the*degree*of*an edge is*the*sum*of**the*degrees*of*its endpoints. ... Acknowledgments*The*authors wish to thank Martine Labbé, with whom this research was initiated, and Hadrien Mélot, author*of**the*GraPHedron software [11] , which was used to formulate*the*initial conjectures ...##
###
Approximation algorithms for multi-dimensional assignment problems with decomposable costs

1994
*
Discrete Applied Mathematics
*

We propose several simple

doi:10.1016/0166-218x(94)90199-6
fatcat:tmu3gtshdjcwlod2ejhqfudcwy
*heuristics*for this problem, and we derive worst-case bounds on*the*ratio between*the*cost*of**the*solutions produced by these*heuristics*and*the*cost*of*an optimal solution. ...*A*clique*of*G is*a*subset*of*vertices meeting each Xi in exactly one vertex.*The*cost*of**a*clique is*a*function*of**the*lengths*of**the*edges induced by*the*clique. ... Hans van der Stel for his assistance in solving some*of**the*difference equations arising in this work. ...##
###
Heuristics with Performance Guarantees for the Minimum Number of Matches Problem in Heat Recovery Network Design
[article]

2018
*
arXiv
*
pre-print

Determining provably good solutions to

arXiv:1709.04688v2
fatcat:srhhmonhqvhzzp3a57no7ysxge
*the*minimum number*of**matches*is*a*bottleneck*of*designing*a*heat recovery network using*the*sequential method. ... Numerical results from*a*collection*of*51 instances substantiate*the*strength*of**the*methods. ... ., and*a*Royal Academy*of*Engineering Research Fellowship to R.M. ...##
###
Reprint of: Heuristics with performance guarantees for the minimum number of matches problem in heat recovery network design

2018
*
Computers and Chemical Engineering
*

Determining provably good solutions to

doi:10.1016/j.compchemeng.2018.10.015
fatcat:ep4uouxtxjf63ii2cfdoyi3bui
*the*minimum number*of**matches*is*a*bottleneck*of*designing*a*heat recovery network using*the*sequential method. ... Numerical results from*a*collection*of*51 instances substantiate*the*strength*of**the*methods. R This manuscript is dedicated, with deepest respect, to*the*memory*of*Professor C.A. Floudas. ... In each iteration,*the**heuristic*chooses*a**match**maximizing**the*additional heat exchanged. ...##
###
Page 571 of Mathematical Reviews Vol. , Issue 95a
[page]

1995
*
Mathematical Reviews
*

*The*assignment problem can be classified as

*a*special

*matching*problem. ... Summary: “

*The*sum

*of*squares

*of*

*the*edge lengths

*of*

*the*tour provided by

*the*spacefilling curve

*heuristic*applied to

*a*random sample

*of*n points from

*the*unit square is proved to be asymptot- ically equal ...

##
###
Heuristics with performance guarantees for the minimum number of matches problem in heat recovery network design

2018
*
Computers and Chemical Engineering
*

Determining provably good solutions to

doi:10.1016/j.compchemeng.2018.03.002
fatcat:ou55opioojhr7o6heew3sath4y
*the*minimum number*of**matches*is*a*bottleneck*of*designing*a*heat recovery network using*the*sequential method. ... Numerical results from*a*collection*of*51 instances substantiate*the*strength*of**the*methods. ... ., and*a*EPSRC EP/P016871/1 Research Fellowship to R.M. ...##
###
Approximation Algorithms for Multi-Dimensional Vector Assignment Problems

2013
*
Social Science Research Network
*

We provide examples to illustrate

doi:10.2139/ssrn.2381949
fatcat:jw2qa72z5nfj5dp4dqjcvjnoay
*the**tightness**of*our*analysis*. Furthermore, we show that*the*MVA problem is APX-hard even for*the*case m = 3 and for binary input vectors. ... An instance*of**the*MVA problem is defined by m disjoint sets, each*of*which contains*the*same number n*of*p-dimensional vectors with nonnegative integral components, and*a*cost function defined on vectors ...*The*project leading to these results was partially funded by OT Grant OT/07/015 and by*the*Interuniversity Attraction Poles Programme initiated by*the*Belgian Science Policy Office, Grant P7/36. ...##
###
Approximating Minimum-Size k-Connected Spanning Subgraphs via Matching

2000
*
SIAM journal on computing (Print)
*

*The*

*heuristic*is based on

*a*subroutine for

*the*degree-constrained subgraph (b-

*matching*) problem. It is simple and deterministic and runs in time O(k|E| 2 ). ...

*The*following result on simple undirected graphs is used in

*the*

*analysis*:

*The*number

*of*edges required for augmenting

*a*graph

*of*minimum degree k to be k-edge connected is at most k |V |/(k+1). ...

*The*

*analysis*

*of*

*the*

*heuristic*for graphs hinges on

*a*deep theorem

*of*Mader [Ma 72, Theorem 1]. ...

##
###
Computational Intelligence Based Decision Support Tool for Personalized Advertisement Assignment System

2013
*
International Journal of Computational Intelligence Systems
*

*The*performance

*of*these

*heuristics*was tested with an experimental

*analysis*. ...

*The*objective

*of*

*the*research was both development

*of*

*a*novel business model and

*the*framework. Four

*heuristics*are proposed as part

*of*

*the*framework. ... Numerical Studies and Discussions An experimental

*analysis*was conducted in order to test

*the*performance

*of*

*the*proposed

*heuristics*. ...

##
###
Approximation Algorithms for the Wafer to Wafer Integration Problem
[chapter]

2013
*
Lecture Notes in Computer Science
*

We argue that

doi:10.1007/978-3-642-38016-7_23
fatcat:ximoxc3gpvghbhicwgvckzvlk4
*a*special case*of**the*yield optimization problem can be solved in polynomial time. ... Motivated by*the*yield optimization problem in semiconductor manufacturing, we model*the*wafer to wafer integration problem as*a*special multi-dimensional assignment problem (called WWI-m), and study it ... Let us call x (y)*the*amount with which*the*value*of**a*partial optimal (*heuristic*) solution increases when vectors from V 3 are*matched*optimally to*the*optimal (*heuristic*) pairs from V 1 × V 2 . ...##
###
Page 6182 of Mathematical Reviews Vol. , Issue 91K
[page]

1991
*
Mathematical Reviews
*

Sci., 202, Springer, Berlin, 1985; MR 87f:68056] that

*the*problem would be tractable when*the**maximal*number*of*repetitions*of**a*variable is fixed. ... We improve*the*lower bound*of**the*first-fit-decreasing*heuristic*when m > 5 and m is odd, and prove that this*heuristic*is optimal when m = 2 if each item has at least one coordinate larger than 5. ...##
###
Multi-dimensional vector assignment problems

2014
*
Discrete Optimization
*

We provide examples to illustrate

doi:10.1016/j.disopt.2014.08.005
fatcat:5vusjuzf2jcpvkouwhbc345lcu
*the**tightness**of*our*analysis*. Furthermore, we show that*the*MVA problem is APX-hard even for*the*case m = 3 and for binary input vectors. ... We consider*a*particular class*of*polynomial-time*heuristics*for MVA, namely*the*sequential*heuristics*, and we study their approximation ratio. ... We gratefully acknowledge useful comments by*the*reviewers*of**a*first version*of**the*paper. ...
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