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Complexity of majority monopoly and signed domination problems

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. ...

##
###
Minimum monopoly in regular and tree graphs

2006
*
Discrete Mathematics
*

We show this by establishing two L-reductions (an

doi:10.1016/j.disc.2005.06.036
fatcat:ebljfyhdfra6laxw2i2c7nmjte
*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. ...##
###
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

2002
*
Algorithmica
*

In case there is no solution for E, we want to maximize

doi:10.1007/s00453-002-0963-8
fatcat:qmbptbs2trgillgpli7zzpw2r4
*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. ...##
###
Max- and Min-Neighborhood Monopolies
[chapter]

2000
*
Lecture Notes in Computer Science
*

In case there is no solution for E, we want to maximize

doi:10.1007/3-540-44985-x_43
fatcat:pvd3itgcxbgetjnkdit5nvbnti
*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. ...##
###
Computational Aspects of Multimarket Price Wars
[chapter]

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 ...

##
###
Author index to volume

2004
*
Discrete Applied Mathematics
*

Penna,

doi:10.1016/s0166-218x(04)00032-0
fatcat:3777nuxoureizeibavzy66hyzy
*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. ...##
###
Local majorities, coalitions and monopolies in graphs: a review

2002
*
Theoretical Computer Science
*

This paper provides an overview

doi:10.1016/s0304-3975(01)00055-x
fatcat:iddd6arxgva7bj7rwr4mwjah5a
*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 ...##
###
On some tractable and hard instances for partial incentives and target set selection
[article]

2018
*
arXiv
*
pre-print

We also contribute some new results about target set seletion

arXiv:1805.10086v1
fatcat:nq77z3t4rvgulgqbstujzleqi4
*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. ...##
###
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

2013
*
Discrete Applied Mathematics
*

We prove that these

doi:10.1016/j.dam.2012.10.007
fatcat:ssmp7zkqqnfidccu7k7kerw4aa
*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. ...##
###
Combinatorial model and bounds for target set selection

2010
*
Theoretical Computer Science
*

A Perfect Target Set is a set

doi:10.1016/j.tcs.2010.08.021
fatcat:lrpbxreelrgd7eiltbjwbmlivm
*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*. ...##
###
Partial immunization of trees

2020
*
Discrete Optimization
*

We study

doi:10.1016/j.disopt.2020.100568
fatcat:gaezttkkengahk3tb7yyd7coee
*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 ...##
###
A survey on alliances and related parameters in graphs

English

2014
*
Electronic Journal of Graph Theory and Applications
*

English

Finally, we also give a survey

doi:10.5614/ejgta.2014.2.1.7
fatcat:um6dgoir7fhp3ehk6fm3dmtbg4
*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. ...##
###
Alliances and related parameters in graphs
[article]

2013
*
arXiv
*
pre-print

for

arXiv:1311.4899v1
fatcat:nvwewcrfizc5nojyietet6jum4
*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. ...
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