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Approximating Disjoint-Path Problems Using Greedy Algorithms and Packing Integer Programs
[chapter]

1998
*
Lecture Notes in Computer Science
*

First, we propose simple

doi:10.1007/3-540-69346-7_12
fatcat:gh576xwwcfbelbhh64qu32j5iu
*greedy**algorithms*for edge-*and*vertex-*disjoint**paths**and*second, we propose the*use*of a framework based on*packing**integer**programs*for more general*problems*such as unsplittable ... We introduce techniques which yield new*algorithms*for a wide range of*disjoint*-*path**problems*. We*use*two basic techniques. ... We wish to thank Jon Kleinberg*and*Aravind Srinivasan for valuable discussions. We also thank Javed Aslam for helpful discussions. ...##
###
Page 5952 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

*using*

*greedy*

*algorithms*

*and*

*packing*

*integer*

*programs*. ... First, we propose simple

*greedy*

*algorithms*for edge-

*and*vertex-

*disjoint*

*paths*

*and*second, we propose the

*use*of a framework based on

*packing*

*integer*

*programs*for more gen- eral

*problems*such as unsplittable ...

##
###
Routing, Wavelength Assignment in Optical Networks Using an Efficient and Fair EDP Algorithm
[chapter]

2004
*
Lecture Notes in Computer Science
*

Routing

doi:10.1007/978-3-540-24688-6_152
fatcat:5imsruuybrdbjpg7w2og7rdnfi
*and*wavelength assignment (RWA)*problem*in wavelength routed optical networks is typically solved*using*a combination of*integer**programming**and*graph coloring. ... RWA with maximum edge*disjoint**path*(EDP)*using*simple bounded*greedy**algorithm*is shown to be as good as previously known solution method. ... Simple*greedy**algorithm*for maximum EDP is*used*in [8]*and*it is shown that it performs as good as that of more complex solution methods based on*integer*linear*programming*. ...##
###
Greedy Algorithms for Online Survivable Network Design

2018
*
International Colloquium on Automata, Languages and Programming
*

In particular, we prove that the

doi:10.4230/lipics.icalp.2018.152
dblp:conf/icalp/DehghaniEHLS18
fatcat:iig474zqjzdcbp3aixsze6fwqu
*greedy**algorithm*is O(log 2 n log k)-competitive if one satisfies every demand between u*and*v by r uv /2 edge-*disjoint**paths*. ... The spirit of our result is similar to the work of Chuzhoy*and*Li [7] (FOCS'12), in which the authors give a polylogarithmic*approximation**algorithm*for edge-*disjoint**paths*with congestion 2. ... Acknowledgements The authors would like to thank Seffi Naor for several fruitful discussions about the prophet versions of the online*problems*. ...##
###
Single-Sink Network Design with Vertex Connectivity Requirements

2008
*
Foundations of Software Technology and Theoretical Computer Science
*

In this paper, inspired by the results

doi:10.4230/lipics.fsttcs.2008.1747
dblp:conf/fsttcs/ChekuriK08a
fatcat:gftomgmuyragrj2y2fjqyeiozq
*and*ideas in [4], we show an O(k O(k) log |T|)-*approximation*bound for a simple*greedy**algorithm*. ... The input to these*problems*is an edge-weighted undirected graph G = (V, E), a sink/root vertex r, a set of terminals T ⊆ V,*and**integer*k. ... Acknowledgments: We are grateful to Sanjeev Khanna for several discussions on the kconnectivity*problem**and*for explaining the results*and*ideas in [4] . ...##
###
Exact and Approximation Algorithms for DNA Tag Set Design
[chapter]

2005
*
Lecture Notes in Computer Science
*

Second, we note the benefits of periodic tags,

doi:10.1007/11496656_33
fatcat:bbga4lg7zzgtjh6siywcigbsum
*and*establish an interesting connection between the tag design*problem**and*the*problem*of*packing*the maximum number of vertex-*disjoint*directed cycles in ... First, we give*integer*linear*programming*formulations for two previous formalizations of the tag set design*problem*,*and*show that these formulations can be solved to optimality for instance sizes of ... Settling the*approximation*complexity of Maximum Vertex-*Disjoint*Directed Cycle*Packing*is another interesting*problem*. ...##
###
Exact and Approximation Algorithms for DNA Tag Set Design

2006
*
Journal of Computational Biology
*

Second, we note the benefits of periodic tags,

doi:10.1089/cmb.2006.13.732
pmid:16706722
fatcat:okafmk6aczfkxnzsgbyr72ea74
*and*establish an interesting connection between the tag design*problem**and*the*problem*of*packing*the maximum number of vertex-*disjoint*directed cycles in ... First, we give*integer*linear*programming*formulations for two previous formalizations of the tag set design*problem*,*and*show that these formulations can be solved to optimality for instance sizes of ... Settling the*approximation*complexity of Maximum Vertex-*Disjoint*Directed Cycle*Packing*is another interesting*problem*. ...##
###
Edge-Disjoint Paths and Unsplittable Flow
[chapter]

2007
*
Handbook of Approximation Algorithms and Metaheuristics
*

We call an LP solution for the optimization

doi:10.1201/9781420010749.ch57
fatcat:paocu5ug3rbj7bgn2nscsy6uwy
*problem*of interest fractional. Several early*approximation**algorithms*for Ufp,*and*more generally*integer*multicommodity flow, work in two stages. ... For extended Ufp with polynomially bounded demands, [44] gave a simple randomized*algorithm*that achieves an O( √ m log 3/2 m)-*approximation**and*generalized the*greedy**algorithm*for Edp [62] (cf. ... Thanks to Chandra Chekuri, Sanjeev Khanna, Maren Martens, Martin Skutella,*and*Cliff Stein for valuable comments*and*suggestions. ...##
###
Solving combined configuration problems: a heuristic approach

2015
*
International Configuration Workshop
*

In the paper we show how to formulate a combined configuration

dblp:conf/confws/GebserRS15
fatcat:2adyk47vtzd23axocvbnpxogdm
*problem*in Answer Set*Programming*(ASP)*and*to solve it*using*heuristics à la hclasp. ... Often isolated parts of configuration*problems*can be solved by mapping them to well-studied*problems*for which efficient heuristics exist (graph coloring, bin-*packing*, etc.). ... As an example for solving the complete CCP*problem*, we can, first, find an unconnected solution for the combination of Coloring, Bin-*Packing*,*Disjoint**paths**and*Matching*problems*(P1-P4),*and*then,*use*...##
###
Page 10490 of Mathematical Reviews Vol. , Issue 2004m
[page]

2004
*
Mathematical Reviews
*

Summary: “We consider a

*path**packing**problem*: given a supply graph G with a node-set N*and*a demand graph (7, S$) with T C N, find the maximal number of edge-*disjoint**paths*in G whose end-pairs belong ...*Approximate**and*exact al- gorithms are proposed for several variants of this*problem*. In particular, the one-dimensional version is nontrivial*and*an O(n?)*algorithm*is given. ...##
###
Wavelength Management in WDM Rings to Maximize the Number of Connections

2009
*
SIAM Journal on Discrete Mathematics
*

This is known as the maximum routing

doi:10.1137/06067660x
fatcat:mcvnozzfxrcv3a6bjyr23iuiaa
*and**path*coloring*problem*(maxRPC). Our main contribution is a general analysis method for a class of iterative*algorithms*for a more general coloring*problem*. ... We apply this method to maxRPC in both undirected*and*bidirected rings to obtain bounds on the*approximability*of several*algorithms*. ... of the*algorithm*that is*used*to compute link-*disjoint**paths*. ...##
###
A Branch-Price-and-Cut Algorithm for Packing Cuts in Undirected Graphs

2016
*
ACM Journal of Experimental Algorithmics
*

The cut

doi:10.1145/2851492
fatcat:y6majvyrhrdevlw3k3akboidw4
*packing**problem*in an undirected graph is to find a largest cardinality collection of pairwise edge-*disjoint*cuts. ... We propose a branch-price-*and*-cut*algorithm*to optimally solve instances from various graph classes, random*and*from the literature, with up to several hundred vertices. ... We have made*algorithmic**use*of the combinatorial structure of the*problem*: we*used*min-cut*algorithms*for the pricing*problem*; we computed a combinatorial dual bound for tightening the relaxation;*and*...##
###
A Branch-Price-and-Cut Algorithm for Packing Cuts in Undirected Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

The cut

doi:10.1007/978-3-319-07959-2_4
fatcat:5mfzxx42m5c6zbff6g2d625xbi
*packing**problem*in an undirected graph is to find a largest cardinality collection of pairwise edge-*disjoint*cuts. ... We propose a branch-price-*and*-cut*algorithm*to optimally solve instances from various graph classes, random*and*from the literature, with up to several hundred vertices. ... We have made*algorithmic**use*of the combinatorial structure of the*problem*: we*used*min-cut*algorithms*for the pricing*problem*; we computed a combinatorial dual bound for tightening the relaxation;*and*...##
###
Recognizing Greedy Structures

1996
*
Journal of Algorithms
*

We present

doi:10.1006/jagm.1996.0006
fatcat:t27q2td6u5f5jprsp7mzercu7y
*algorithms*for the recognition of*greedy*instances of certain*problems*, structural characterization of such instances for other*problems*,*and*proofs of NP-hardness of the recognition*problem*... We study decision*problems*of the following form: Given an instance of a combinatorial*problem*, can it be solved by a*greedy**algorithm*? ... A potentially interesting direction might be the recognition of ''*approximately**greedy*'' structures ᎏinstances where the*greedy**algorithm*guarantees to provide a good*approximation*of the optimal goal. ...##
###
Page 7708 of Mathematical Reviews Vol. , Issue 2002J
[page]

2002
*
Mathematical Reviews
*

We extend

*and*refine fractional*packing*frameworks introduced in FPTAS’s for tradi- tional multicommodity flow*and**packing*linear*programs*. ... Summary: “The classical*greedy*heuristic for*approximating*a maximum independent set is simple*and*efficient. ...
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