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Approximating Minimum Dominating Set on String Graphs [article]

Dibyayan Chakraborty, Sandip Das, Joydeep Mukherjee
2018 arXiv   pre-print
In this paper, we give approximation algorithms for the Minimum Dominating Set (MDS) problem on string graphs and its subclasses.  ...  Using our result on SSR-problem, we give a polynomial time O(k^4)-approximation algorithm for MDS problem on unit B_k-VPG graphs for k≥ 0.  ...  The Minimum Dominating Set (MDS) problem is to find a minimum cardinality dominating set of a graph G.  ... 
arXiv:1809.09990v2 fatcat:viiuk4eguzandknoijta7sko7e

Approximation Algorithms for Independence and Domination on B_1-VPG and B_1-EPG Graphs [article]

Saeed Mehrabi
2017 arXiv   pre-print
In this paper, we study the Maximum Independent Set and Minimum Dominating Set problems on B_1-VPG and B_1-EPG graphs.  ...  Then, we consider the Minimum Dominating Set problem.  ...  • Our O(1)-approximation algorithm for Minimum Dominating Set on one-string B 1 -VPG graphs relies on the fact that the input graph is one-string (in the proof of Lemma 4.3, in particular); is there an  ... 
arXiv:1702.05633v1 fatcat:gqrbomsgijahjmg7gs6sj3f6ri

Distributed approximation

Michael Elkin
2004 ACM SIGACT News  
Recently considerable progress was achieved in designing efficient distributed approximation algorithms, and in demonstrating hardness of distributed approximation for various problems.  ...  [17] have shown a series of strikingly elegant lower bounds on the approximability of the minimum vertex cover, the minimum dominating set, and maximum matching problems.  ...  The Minimum Vertex Cover Problem In this section we describe the lower bound of Kuhn et al. [18] on the approximability of the minimum vertex cover and the minimum dominating set problems.  ... 
doi:10.1145/1054916.1054931 fatcat:qibyt3pkpnc6rnchn6ruafglby

The inapproximability of non-NP-hard optimization problems

Liming Cai, David Juedes, Iyad Kanj
2002 Theoretical Computer Science  
Techniques are given to show that the problems LOG DOMINATING SET and LOG HYPERGRAPH VERTEX COVER cannot be approximated to a constant ratio in polynomial time unless the corresponding NP-hard versions  ...  SET and RICH HYPERGRAPH VERTEX COVER.  ...  TOURNAMENT DOMINATING SET: Given a tournament graph G, ÿnd a minimum dominating set for the graph.  ... 
doi:10.1016/s0304-3975(01)00343-7 fatcat:mkrjr5hw3fhh3f3lqaznumhp24

The Inapproximability of Non NP-hard Optimization Problems [chapter]

Liming Cai, David Juedes, Iyad Kanj
1998 Lecture Notes in Computer Science  
Dominating Set: Given a tournament graph G, nd a minimum dominating set for the graph.  ...  Log k Dominating Set: (k 1) Given a directed graph G = (V; E) in which V = fv 1 ; : : :; v n g and subset fv 1 ; ; v log k n g of V forms a dominating set for G, nd a minimum dominating set for G.  ...  (v; v j ) 2 Eg If the original graph G has a dominating set of size hn c , then this dominating set can be partitioned into h disjoint sets D i 1 ; : : :; D i h .  ... 
doi:10.1007/3-540-49381-6_46 fatcat:zstrtvcwnzebbb5qmjl23qkxkq

Unconditional lower bounds on the time-approximation tradeoffs for the distributed minimum spanning tree problem

Michael Elkin
2004 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04  
In this paper we initiate the systematic study of this subject, and show strong unconditional lower bounds on the time-approximation tradeoff of the distributed minimum spanning tree problem, and some  ...  However, so far little progress was done in the study of the hardness of distributed approximation.  ...  Most notably, several approximation protocols were recently devised for the minimum dominating set problem [18, 9, 21] , and for the minimum edge-coloring problem [26, 10, 17, 4] .  ... 
doi:10.1145/1007352.1007407 dblp:conf/stoc/Elkin04 fatcat:6y7k2lp4tjbdzo7af65buplj2i

The Homogeneous Broadcast Problem in Narrow and Wide Strips II: Lower Bounds

Mark de Berg, Hans L. Bodlaender, Sándor Kisfaludi-Bak
2019 Algorithmica  
The (homogeneous) broadcast problem is to activate a minimum number of nodes such that in the resulting directed communication graph, the source s can reach any other node.  ...  Let P be a set of nodes in a wireless network, where each node is modeled as a point in the plane, and let s ∈ P be a given source node.  ...  Overview of Our Construction for CONNECTED DOMINATING SET in Unit Disk Graphs To extend the construction to Connected Dominating Set in Unit Disk Graphs, we have to make sure there is a minimum-size dominating  ... 
doi:10.1007/s00453-019-00561-0 fatcat:7qrqlzyr3nac7lt2xxzfb7j22a

Approximation Hardness of Minimum Edge Dominating Set and Minimum Maximal Matching [chapter]

Miroslav Chlebík, Janka Chlebíková
2003 Lecture Notes in Computer Science  
We provide the first interesting explicit lower bounds on efficient approximability for two closely related optimization problems in graphs, Minimum Edge Dominating Set and Minimum Maximal Matching.  ...  The result extends with negligible loss to bounded degree graphs and to everywhere dense graphs.  ...  In fact, the minimum cardinality of edge dominating sets in G is achieved also on maximal matchings in G.  ... 
doi:10.1007/978-3-540-24587-2_43 fatcat:5hnr62moxfenrcyv7f5fpfta5e

Approximating Independent Set and Dominating Set on VPG graphs [article]

Esther Galby, Andrea Munaro
2020 arXiv   pre-print
We consider Independent Set and Dominating Set restricted to VPG graphs (or, equivalently, string graphs).  ...  We show that they both remain NP-hard on B_0-VPG graphs admitting a representation such that each grid-edge belongs to at most one path and each horizontal path has length at most two.  ...  SET on string graphs.  ... 
arXiv:2004.07566v1 fatcat:s6h7fmw5pbentmrjocamapbxsy

Techniques for Practical Fixed-Parameter Algorithms

F. Huffner, R. Niedermeier, S. Wernicke
2007 Computer journal  
Focusing on their application to solving NP-hard problems in practice, we survey three main techniques to develop fixed-parameter algorithms, namely: kernelization (data reduction with provable performance  ...  in the input graph such that at least one of these vertices must be in a minimum-size dominating set and then branch on putting parts of it into the dominating set.  ...  DOMINATING SET in general graphs.  ... 
doi:10.1093/comjnl/bxm040 fatcat:jbffitiefzfexftg3lgl7xnsza

The Intractability of Computing the Hamming Distance [chapter]

Bodo Manthey, Rüdiger Reischuk
2003 Lecture Notes in Computer Science  
Given a string x and a language L, the Hamming distance of x to L is the minimum Hamming distance of x to any string in L. The edit distance of a string to a language is analogously defined.  ...  First, we prove that there is a language in AC 0 such that both Hamming and edit distance to this language are hard to approximate; they cannot be approximated with a factor O(n 1 3 − ), for any > 0, unless  ...  problem Minimum Independent Dominating Set (MIDS).  ... 
doi:10.1007/978-3-540-24587-2_11 fatcat:mokzwmgp3rbm5aep6uhx22fkdi

Linear approximation of shortest superstrings

Avrim Blum, Tao Jiang, Ming Li, John Tromp, Mihalis Yannakakis
1991 Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91  
with maximum overlap until only one string remains.  ...  We show that the greedy algorithm does in fact achieve a constant factor approximation, proving an upper bound of 4n.  ...  Let CYC(G S ) be the weight of the minimum assignment on graph G S , so CYC(G S ) TSP(G S ) OPT(S).  ... 
doi:10.1145/103418.103455 dblp:conf/stoc/BlumJLTY91 fatcat:rrhuzscoezfe7o6vh42lte2bvy

Linear approximation of shortest superstrings

Avrim Blum, Tao Jiang, Ming Li, John Tromp, Mihalis Yannakakis
1994 Journal of the ACM  
with maximum overlap until only one string remains.  ...  We show that the greedy algorithm does in fact achieve a constant factor approximation, proving an upper bound of 4n.  ...  Let CYC(G S ) be the weight of the minimum assignment on graph G S , so CYC(G S ) TSP(G S ) OPT(S).  ... 
doi:10.1145/179812.179818 fatcat:cc4wxhdpavd7bdjdxrjmxfycau

Approximating Optimization Problems using EAs on Scale-Free Networks [article]

Ankit Chauhan and Tobias Friedrich and Francesco Quinzan
2018 arXiv   pre-print
a constant-factor approximation ratio on the Minimum Dominating Set problem, the Minimum Vertex Cover problem, the Minimum Connected Dominating Set problem, and the Maximum Independent Set problem in  ...  We observe that on scale-free networks, simple evolutionary algorithms (EAs) quickly reach a constant-factor approximation ratio on common covering problems We prove that the single-objective (1+1)EA reaches  ...  cardinality, until a good approximation of a minimum dominating set is reached.  ... 
arXiv:1704.03664v3 fatcat:clmmumzz5bco3o34uoxvm55ipy

A Note on Approximating Weighted Independence on Intersection Graphs of Paths on a Grid [article]

Saeed Mehrabi
2018 arXiv   pre-print
In this paper, we study the Maximum-Weighted Independent Set problem on B_k-VPG graphs.  ...  A graph G is called B_k-VPG, for some constant k≥ 0, if it has a string representation on an axis-parallel grid such that each vertex is a path with at most k bends and two vertices are adjacent in G if  ...  For instance, Minimum Dominating Set problem is APX-hard on one-string B 1 -VPG graphs 1 due to the facts that every circle graph is a one-string B 1 -VPG graph [1] and that Minimum Dominating Set is  ... 
arXiv:1708.09314v2 fatcat:mlttduwv7bairo6c5tga7pj3sm
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