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

Stavros G. Kolliopoulos, Clifford Stein
1998 Lecture Notes in Computer Science  
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 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.  ... 
doi:10.1007/3-540-69346-7_12 fatcat:gh576xwwcfbelbhh64qu32j5iu

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]

Pallavi Manohar, V. Sridhar
2004 Lecture Notes in Computer Science  
Routing 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.  ... 
doi:10.1007/978-3-540-24688-6_152 fatcat:5imsruuybrdbjpg7w2og7rdnfi

Greedy Algorithms for Online Survivable Network Design

Sina Dehghani, Soheil Ehsani, MohammadTaghi Hajiaghayi, Vahid Liaghat, Saeed Seddighin, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming  
In particular, we prove that the 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.  ... 
doi:10.4230/lipics.icalp.2018.152 dblp:conf/icalp/DehghaniEHLS18 fatcat:iig474zqjzdcbp3aixsze6fwqu

Single-Sink Network Design with Vertex Connectivity Requirements

Chandra Chekuri, Nitish Korula, Marc Herbstritt
2008 Foundations of Software Technology and Theoretical Computer Science  
In this paper, inspired by the results 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] .  ... 
doi:10.4230/lipics.fsttcs.2008.1747 dblp:conf/fsttcs/ChekuriK08a fatcat:gftomgmuyragrj2y2fjqyeiozq

Exact and Approximation Algorithms for DNA Tag Set Design [chapter]

Ion I. Măndoiu, Dragoş Trincă
2005 Lecture Notes in Computer Science  
Second, we note the benefits of periodic tags, 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.  ... 
doi:10.1007/11496656_33 fatcat:bbga4lg7zzgtjh6siywcigbsum

Exact and Approximation Algorithms for DNA Tag Set Design

Ion I. Măndoiu, Dragoş Trincă
2006 Journal of Computational Biology  
Second, we note the benefits of periodic tags, 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.  ... 
doi:10.1089/cmb.2006.13.732 pmid:16706722 fatcat:okafmk6aczfkxnzsgbyr72ea74

Edge-Disjoint Paths and Unsplittable Flow [chapter]

Stavros Kolliopoulos
2007 Handbook of Approximation Algorithms and Metaheuristics  
We call an LP solution for the optimization 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.  ... 
doi:10.1201/9781420010749.ch57 fatcat:paocu5ug3rbj7bgn2nscsy6uwy

Solving combined configuration problems: a heuristic approach

Martin Gebser, Anna Ryabokon, Gottfried Schenner
2015 International Configuration Workshop  
In the paper we show how to formulate a combined configuration 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  ... 
dblp:conf/confws/GebserRS15 fatcat:2adyk47vtzd23axocvbnpxogdm

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

Ioannis Caragiannis
2009 SIAM Journal on Discrete Mathematics  
This is known as the maximum routing 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.  ... 
doi:10.1137/06067660x fatcat:mcvnozzfxrcv3a6bjyr23iuiaa

A Branch-Price-and-Cut Algorithm for Packing Cuts in Undirected Graphs

Martin Bergner, Marco E. LÜbbecke, Jonas T. Witt
2016 ACM Journal of Experimental Algorithmics  
The cut 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  ... 
doi:10.1145/2851492 fatcat:y6majvyrhrdevlw3k3akboidw4

A Branch-Price-and-Cut Algorithm for Packing Cuts in Undirected Graphs [chapter]

Martin Bergner, Marco E. Lübbecke, Jonas T. Witt
2014 Lecture Notes in Computer Science  
The cut 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  ... 
doi:10.1007/978-3-319-07959-2_4 fatcat:5mfzxx42m5c6zbff6g2d625xbi

Recognizing Greedy Structures

Yair Caro, András Sebő, Michael Tarsi
1996 Journal of Algorithms  
We present 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.  ... 
doi:10.1006/jagm.1996.0006 fatcat:t27q2td6u5f5jprsp7mzercu7y

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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