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Complexity of majority monopoly and signed domination problems

Sounaka Mishra
2012 Journal of Discrete Algorithms  
On the other hand, given a graph G = (V , E), in the signed domination problem one needs to find a function f : We show that minimum majority monopoly and minimum signed domination cannot be approximated  ...  On the positive side, we give ln( + 1)-factor approximation algorithm for minimum majority monopoly problem for general graphs.  ...  Acknowledgement The author thanks the anonymous referees for their valuable comments and suggestions that helped to improve the clarity, correctness and presentation of the proofs.  ... 
doi:10.1016/j.jda.2011.12.019 fatcat:zcrilcdbjnhmzczcay2hu7esei

Minimum monopoly in regular and tree graphs

S. Mishra, S.B. Rao
2006 Discrete Mathematics  
We show this by establishing two L-reductions (an approximation preserving reduction) from minimum dominating set problem for k-regular graphs to minimum monopoly problem for 2k-regular graphs and to minimum  ...  In this paper we consider a graph optimization problem called minimum monopoly problem, in which it is required to find a minimum cardinality set S ⊆ V , such that, for each u ∈ V , |N [u] ∩ S| |N[u]|/  ...  A problem ∈ NPO is APX-hard if, for any ∈ APX, L , and problem is APX-complete if is APX-hard and ∈ APX.  ... 
doi:10.1016/j.disc.2005.06.036 fatcat:ebljfyhdfra6laxw2i2c7nmjte

Page 9195 of Mathematical Reviews Vol. , Issue 2004k [page]

2004 Mathematical Reviews  
[Mishra, Sounaka] (6-MATSCI; Chennai) ; Radhakrishnan, Jaikumar (6-TIFR-STC; Mumbai); Sivasubramanian, S. (6-TIFR-STC; Mumbai) On the hardness of approximating minimum monopoly problems.  ...  Finally, for cubic graphs, we give a 1.6154 approximation algorithm for the monopoly problem and a : approximation algorithm for the par- tial monopoly problem, and show that they are APX-complete.”  ... 

Max- and Min-Neighborhood Monopolies

Makino, Yamashita, Kameda
2002 Algorithmica  
In case there is no solution for E, we want to maximize the number of vertices controlled by the given M . Unfortunately, this problem turns out to be NP-hard.  ...  We, therefore, design a simple approximation algorithm which guarantees an approximation ratio of 2.  ...  As for computational complexity, Peleg [11] showed that the problem of computing a minimum monopoly is NP-hard, by reducing the minimum dominating set problem to it.  ... 
doi:10.1007/s00453-002-0963-8 fatcat:qmbptbs2trgillgpli7zzpw2r4

Max- and Min-Neighborhood Monopolies [chapter]

Kazuhisa Makino, Masafumi Yamashita, Tiko Kameda
2000 Lecture Notes in Computer Science  
In case there is no solution for E, we want to maximize the number of vertices controlled by the given M . Unfortunately, this problem turns out to be NP-hard.  ...  We, therefore, design a simple approximation algorithm which guarantees an approximation ratio of 2.  ...  As for computational complexity, Peleg [11] showed that the problem of computing a minimum monopoly is NP-hard, by reducing the minimum dominating set problem to it.  ... 
doi:10.1007/3-540-44985-x_43 fatcat:pvd3itgcxbgetjnkdit5nvbnti

Computational Aspects of Multimarket Price Wars [chapter]

Nithum Thain, Adrian Vetta
2009 Lecture Notes in Computer Science  
On the negative side we show that, even with complete information, it is hard to obtain any multiplicative approximation guarantee for this problem.  ...  Moreover, these hardness results hold even in the simple case of linear demand, price, and cost functions.  ...  The hardness results of Section 4.3 imply that no multiplicative approximation guarantee can be obtained for the Minimum War Chest Problem, even in the simple case of linear cost, price, and demand functions  ... 
doi:10.1007/978-3-642-10841-9_28 fatcat:pq3xp47whjcmnanxr7wn6ef3xy

Author index to volume

2004 Discrete Applied Mathematics  
Penna, On-line algorithms for the channel assignment problem in cellular networks (3) 237-266 Damaschke, P., Approximate location of relevant variables under the crossover distribution (1) 47-67  ...  Yamazaki, Hardness of approximation for non-overlapping local alignments (3) 293-309 Nomura, K., see T. Yamada (2) 225-237 Pagli, L., see P. Flocchini (2) 197-213 Penna, P., see P.  ... 
doi:10.1016/s0166-218x(04)00032-0 fatcat:3777nuxoureizeibavzy66hyzy

Local majorities, coalitions and monopolies in graphs: a review

David Peleg
2002 Theoretical Computer Science  
This paper provides an overview of recent developments concerning the process of local majority voting in graphs, and its basic properties, from graph theoretic and algorithmic standpoints.  ...  The greedy algorithm yields a ratio ln|E| + 1 approximation for the minimum monopoly problem.  ...  In fact, given recent results [47, 20] on the hardness of approximating the set cover problem and its variants, including the minimum dominating set problem, it is plausible to make the following conjecture  ... 
doi:10.1016/s0304-3975(01)00055-x fatcat:iddd6arxgva7bj7rwr4mwjah5a

On some tractable and hard instances for partial incentives and target set selection [article]

Stefan Ehard, Dieter Rautenbach
2018 arXiv   pre-print
We also contribute some new results about target set seletion on planar graphs by showing the hardness of this problem, and by describing an efficient O(√(n))-approximation algorithm as well as a PTAS  ...  for the dual problem of finding a maximum degenerate set.  ...  Complementing our hardness result for dynamic monopolies in planar graphs, we contribute approximation algorithms.  ... 
arXiv:1805.10086v1 fatcat:nq77z3t4rvgulgqbstujzleqi4

Page 1507 of Harvard Law Review Vol. 70, Issue 8 [page]

1957 Harvard Law Review  
Kaysen is explicit on this matter too. There are three aspects to the problem, one relating to diagnosis of market power and two relating to the standard for holding such power illegal.  ...  Ideally such a diagnosis might be made solely on the basis of market-structure evidence (the market share of the defendant, the number and relative sizes of the other firms in the market, the minimum efficient  ... 

On the approximability and exact algorithms for vector domination and related problems in graphs

Ferdinando Cicalese, Martin Milanič, Ugo Vaccaro
2013 Discrete Applied Mathematics  
We prove that these problems (and several variants thereof) cannot be approximated to within a factor of clnn, where c is a suitable constant and n is the number of the vertices, unless P = NP.  ...  We also show that two natural greedy strategies have approximation factors ln D+O(1), where D is the maximum degree of the input graph.  ...  Strictly related to our results is also the paper [12] . The authors study the hardness of approximating minimum monopolies in graphs.  ... 
doi:10.1016/j.dam.2012.10.007 fatcat:ssmp7zkqqnfidccu7k7kerw4aa

Combinatorial model and bounds for target set selection

Eyal Ackerman, Oren Ben-Zwi, Guy Wolfovitz
2010 Theoretical Computer Science  
A Perfect Target Set is a set of vertices whose activation will eventually activate the entire graph, and the Perfect Target Set Selection Problem (PTSS) asks for the minimum such initial set.  ...  This allows one to use standard integer programming solvers for solving small-size PTSS instances. We also show combinatorial lower and upper bounds on the size of the minimum Perfect Target Set.  ...  Given that Target Set Selection is NP-hard, one would like to obtain good approximations for Minimum Target Set and Maximum Active Set. However, both problems turned out to be hard to approximate.  ... 
doi:10.1016/j.tcs.2010.08.021 fatcat:lrpbxreelrgd7eiltbjwbmlivm

Partial immunization of trees

Mitre C. Dourado, Stefan Ehard, Lucia D. Penso, Dieter Rautenbach
2020 Discrete Optimization  
We study the problem of maximizing the minimum order of a dynamic monopoly by increasing the threshold values of individual vertices subject to vertex-dependent lower and upper bounds, and fixing the total  ...  For a graph G and a non-negative integer-valued function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ (u) neighbors  ...  We study the problem of maximizing the minimum order of a dynamic monopoly by increasing the threshold values of individual vertices subject to vertex-dependent lower and upper bounds, and fixing the total  ... 
doi:10.1016/j.disopt.2020.100568 fatcat:gaezttkkengahk3tb7yyd7coee

A survey on alliances and related parameters in graphs
English

Henning Fernau, Juan A. Rodrıguez-Velazquez
2014 Electronic Journal of Graph Theory and Applications  
Finally, we also give a survey on the mentioned graph parameters, indicating how results transfer due to our observations. . We consider several variants of dominating sets.  ...  To help retrieve information on alliance parameters and related notions motivated us to write this type of overview paper.  ...  [47, 48] show that (partial) monopolies no bigger than c times the minimum can be found in polynomial time in cubic graphs, but no PTAS exists on graphs of bounded degree. S. Mishra et al.  ... 
doi:10.5614/ejgta.2014.2.1.7 fatcat:um6dgoir7fhp3ehk6fm3dmtbg4

Alliances and related parameters in graphs [article]

Henning Fernau, Juan A. Rodriguez-Velazquez
2013 arXiv   pre-print
for the study of alliances and domination.  ...  Finally, we also give a survey on the mentioned graph parameters, indicating how results transfer due to our observations.  ...  [47, 48] show that (partial) monopolies no bigger than c times the minimum can be found in polynomial time in cubic graphs, but no PTAS exists on graphs of bounded degree. S. Mishra et al.  ... 
arXiv:1311.4899v1 fatcat:nvwewcrfizc5nojyietet6jum4
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