NC-Approximation Schemes for NP- and PSPACE-Hard Problems for Geometric Graphs
Citations
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Additional excerpts
...Graphs with this restriction have also been called civilized [7] or λ-precision [13] graphs in the literature....
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616 citations
Cites background from "NC-Approximation Schemes for NP- an..."
...In this case, the underlying communication graph, is a Unit Disk graph – defined in [20], [21] in terms of “distance” or “proximity” models, which consist of...
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430 citations
Cites methods from "NC-Approximation Schemes for NP- an..."
...To the best of our knowledge, these proofs are either built for the UDG model [15, 19], or for the abstract SINR model (SINRA), and present reductions without a geometric representation....
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398 citations
Cites background or methods from "NC-Approximation Schemes for NP- an..."
...Following the approach in [16], we now show that MWKVMP and, therefore, MKVMP admits a constant factor PTAS when restricted to geometric graphs....
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...For more discussion on such techniques and their analysis, we refer the reader to [16]....
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...Using arguments similar to [16, 15], we then show that the iteration in which the partition yields a K-valid matching of maximum possible weight returns a K-valid matching...
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...NC-approximation schemes for various NP-Hard and PSPACE-Hard problems restricted to geometric graphs are developed in [16]....
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304 citations
Cites background from "NC-Approximation Schemes for NP- an..."
...Maximum Independent Set for unit disks |x|O(1/ ) [71] [83] Maximum Independent Set for unit squares |x|O(1/ ) [71] [83] Minimum Dominating Set for unit disks |x|O(1/ ) [71] [87] Minimum Dominating Set for unit squares |x|O(1/ ) [71] [87]...
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...The first four lines in Table 2 show that if we restrict Maximum Independent Set and Minimum Dominating Set to the intersection graphs of unitradius disks or unit-size squares, then the problem admits a PTAS [71, 94, 93], but does not have an EPTAS [83, 87]....
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...[71] show that Maximum Independent Set for unit disk graphs admits an |x|O(1/ ) time PTAS....
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References
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