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The non-approximability of bicriteria network design problems

Vojtech Bálint
2003 Journal of Discrete Algorithms  
We prove that this problem is nonapproximable, even in some special cases. Similar results are proved if the stretch factor or the root stretch factor is considered instead of the diameter.  ...  We want to minimize the diameter of a spanning subgraph S (under d-cost) subject to the constraint that the total cost of the edges in S (with respect to c) does not exceed a given budget.  ...  Acknowledgement We thank the anonymous referees for their careful reading and many useful comments, which led to an improvement of the paper.  ... 
doi:10.1016/s1570-8667(03)00033-9 fatcat:czkqvz44qff5hehdfw5as7nc6y

Subject Index

2003 Journal of Discrete Algorithms  
con- straints, 303 Network design The non-approximability of bicriteria network de- sign problems, 339 Non-aproximability The non-approximability of bicriteria network de- sign problems, 339 NP-complete  ...  network de- sign problems, 339 Steiner problem On reductions for the Steiner Problem in Graphs, 77 Stretch factor The non-approximability of bicriteria network de- sign problems, 339 String Lyndon-like  ... 
doi:10.1016/s1570-8667(03)00075-3 fatcat:icg7if3uingibmjwy2mjud4rwe

Bicriteria Network Design Problems [article]

Madhav V. Marathe, R. Ravi, Ravi Sundaram,S. S. Ravi, Daniel J. Rosenkrantz, Harry B. Hunt III
1998 arXiv   pre-print
We study a general class of bicriteria network design problems.  ...  Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria.  ...  We thank Sven Krumke (University of Würzberg) for reading the paper carefully and providing several useful comments. In particular, both pointed an error in the original proof of Theorem 5.3.  ... 
arXiv:cs/9809103v1 fatcat:kgal233ohncypjtkchs3asiabu

Approximation Algorithms for Degree-Constrained Minimum-Cost Network-Design Problems [chapter]

R. Ravi, Madhav V. Marathe, S. S. Ravi, Daniel J. Rosenkrantz, Harry B. Hunt
2009 Fundamental Problems in Computing  
We study network-design problems with two different design objectives: the total cost of the edges and nodes in the network and the maximum degree of any node in the network.  ...  of each vertex § Following the framework developed in [21], a generic bicriteria network design problem, denoted by £ ¦¡ ¦¢ © , is defined by identifying two minimization objectives, denoted by A and  ...  Acknowledgments: We thank the referee for several valuable suggestions. We gratefully acknowledge helpful conversations with M. X. Goemans, P. N. Klein, G. Konjevod, S. Krumke, B. Raghavachari, V. S.  ... 
doi:10.1007/978-1-4020-9688-4_9 dblp:conf/birthday/0001MRRH13 fatcat:axlg2cutrvfefon5vphxjv7qp4

Lower-bounded facility location

Zoya Svitkina
2010 ACM Transactions on Algorithms  
The main technical idea for the design of the algorithm is a reduction to the capacitated facility location problem, which has known constant-factor approximation algorithms.  ...  This problem was introduced independently in the papers by Karger and Minkoff [12] and by Guha, Meyerson, and Munagala [7], both of which give bicriteria approximation algorithms for it.  ...  [7] , who use it as a subroutine for solving the access network design problem.  ... 
doi:10.1145/1824777.1824789 fatcat:alr4lw46gvfvvn3246ydlitc6e

Network performance improvement through evaluation of bicriteria routing methods in transport networks

Lucia Martins, Joao Lopes, Jose Craveirinha, Joao Climaco, Ricardo Cadime, Catarina Monica
2013 Proceedings of the 9th International Conference on Network and Service Management (CNSM 2013)  
In this paper we present a bicriteria approach in which the first objective has the purpose of better distribute the traffic in the network and the second objective function intends to minimize the amount  ...  of the networks still have available bandwidth.  ...  ACKNOWLEDGMENT This work has been partially supported by PT Inovação R&D Project "Optimization in networks with traffic engineering", by programme COMPETE of the EC Community Support Framework III and  ... 
doi:10.1109/cnsm.2013.6727807 dblp:conf/cnsm/MartinsLCCCM13 fatcat:xq7tsxuzsjckjghn6hppkaw5au

Approximation Algorithms for Degree-Constrained Minimum-Cost Network-Design Problems

R. Ravi, M. V. Marathe, S. S. Ravi, D. J. Rosenkrantz, H. B. Hunt III
2001 Algorithmica  
We study network-design problems with two different design objectives: the total cost of the edges and nodes in the network and the maximum degree of any node in the network.  ...  Our main result is a bicriteria approximation algorithm whose output is approximate in terms of both the degree and cost criteria -the degree of any node Ú ¾ Î in the output Steiner tree is Ç´ ´Úµ ÐÓ µ  ...  Acknowledgments: We thank the referee for several valuable suggestions. We gratefully acknowledge helpful conversations with M. X. Goemans, P. N. Klein, G. Konjevod, S. Krumke, B. Raghavachari, V. S.  ... 
doi:10.1007/s00453-001-0038-2 fatcat:nz7kpbttwfeprisjdh5vc27gdm

Compact location problems with budget and communication constraints [chapter]

S. O. Krumke, H. Noltemeier, S. S. Ravi, M. V. Marathe
1995 Lecture Notes in Computer Science  
We consider the problem of placing a speci ed number p of facilities on the nodes of a given network with two nonnegative edge{ weight functions so as to minimize the diameter of the placement with respect  ...  We also present e cient approximation algorithms for several of the problems studied, when both edge{weight functions obey the triangle inequality.  ...  We refer the reader to MR+95, RMR + 93] for a detailed survey of the work done in the area of algorithms for bicriteria network design and location theory problems.  ... 
doi:10.1007/bfb0030872 fatcat:j5h2ydjas5f4plgif7nfydfta4

Approximation Algorithms for the Traveling Purchaser Problem and Its Variants in Network Design [chapter]

R. Ravi, F. S. Salman
1999 Lecture Notes in Computer Science  
For a special case of the problem that models the ring-star network design problem, we g i v e a constant-factor approximation algorithm. Our algorithms are based on rounding LP relaxation solutions.  ...  The traveling purchaser problem is a generalization of the traveling salesman problem with applications in a wide range of areas including network design and scheduling.  ...  Hassin for proving the NP-hardness of the (A + T 1) problem and other helpful discussions. We also thank G. Konjevod for pointing out the direct reduction of TPP to a group Steiner tour problem.  ... 
doi:10.1007/3-540-48481-7_4 fatcat:yb57bgkwq5gerfew3j72dc5rru

On Survivable Set Connectivity [chapter]

Parinya Chalermsook, Fabrizio Grandoni, Bundit Laekhanukit
2014 Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms  
If all sets S i and T i have cardinality 1, SSC is equivalent to the Survivable Network Design problem (a.k.a. Steiner Network problem).  ...  An interesting question is whether one could obtain poly-logarithmic bicriteria approximations for other network design problems whose hardness are derived from MLC.  ...  Now we proceed to the formal proof. Proof. (of Theorem 1.2) Assume by contradiction that the claim is not true, and let A be an (α, β)approximation algorithm that contradicts the claim.  ... 
doi:10.1137/1.9781611973730.3 dblp:conf/soda/ChalermsookGL15 fatcat:ktvq6hucbbg3rlf3335yi4hm44

Finding Densest k-Connected Subgraphs [article]

Francesco Bonchi, David García-Soriano, Atsushi Miyauchi, Charalampos E. Tsourakakis
2020 arXiv   pre-print
For both problems, we propose polynomial-time (bicriteria and ordinary) approximation algorithms, using classic Mader's theorem in graph theory and its extensions.  ...  One of the most well-studied optimization problems for dense subgraph discovery is the densest subgraph problem, where given an edge-weighted undirected graph G=(V,E,w), we are asked to find S⊆ V that  ...  ., and C.T. acknowledge support from Intesa Sanpaolo Innovation Center, who had no role in study design, data collection and analysis, decision to publish, or preparation of the  ... 
arXiv:2007.01533v1 fatcat:qqmg37khlzhz7ijhvv5djzut3q

A study on the minimum subgraph diameter problem

Arthur Pratti Dadalto, Fabio Luiz Usberti, Mário César San Felice
2018 Revista dos Trabalhos de Iniciação Científica da UNICAMP  
This work addresses the minimum subgraph diameter problem (MSDP), an NP-hard problem.  ...  We prove that there is no β-approximation algorithm for the MSDP, for any constant β unless P = NP.  ...  Plesnik, J. (1981), The complexity of designing a network with minimum diameter. Networks, 11: 77-85. 2 Bálint, V. (2003). The non-approximability of bicriteria network design problems.  ... 
doi:10.20396/revpibic262018174 fatcat:i77vuliigjg3hiyp624tg4jsue

Complexity and approximability of certain bicriteria location problems [chapter]

S. O. Krumke, H. Noltemeier, S. S. Ravi, M. V. Marathe
1995 Lecture Notes in Computer Science  
We investigate the complexity and approximability of some location problems when two distance values are speci ed for each pair of potential sites.  ...  These problems involve the selection of a speci ed number of facilities (i.e. a placement of a speci ed size) to minimize a function of one distance metric subject to a budget constraint on the other distance  ...  We refer the reader to MR + 95, RMR + 93] for a survey of the work done in the area of algorithms for bicriteria network design and location theory problems.  ... 
doi:10.1007/3-540-60618-1_67 fatcat:cbrucbhhe5geloelrofiemrewa

Author Index

2003 Journal of Discrete Algorithms  
., The non-approximability of bicriteria network design problems (1) 339 Bespamyatnikh, S. and Kelarev, A., Algorithms for shortest paths and d-cycle problems (1) 1 Boldi, P. and Vigna, S., Lower bounds  ...  , F., On-line algorithms for networks of temporal constraints (1) 303 Daykin, D.E. and Daykin, J.W., Lyndon-like and Vorder factorizations of strings (1) 357 Daykin, J.W., see Daykin, D.E. (1) 357 Dinitz  ... 
doi:10.1016/s1570-8667(03)00074-1 fatcat:2ps4z5nqxvhddpzmztebbqb26e

Structural Rounding: Approximation Algorithms for Graphs Near an Algorithmically Tractable Class

Erik D. Demaine, Timothy D. Goodrich, Kyle Kloster, Brian Lavallee, Quanquan C. Liu, Blair D. Sullivan, Ali Vakilian, Andrew Van Der Poel, Michael Wagner
2019 European Symposium on Algorithms  
algorithms which simultaneously approximate both the number of editing operations and the target parameter of the family).  ...  We also prove complementary hardness-of-approximation results assuming P = NP: in particular, these problems are all log-factor inapproximable, except the last which is not approximable below some constant  ...  on the manuscript.  ... 
doi:10.4230/lipics.esa.2019.37 dblp:conf/esa/DemaineGKLLSVP19 fatcat:sa6gr2pm3rggpdb5pehdxtmk6e
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