Polynomial Space Algorithms for Counting Dominating Sets and the Domatic Number

Rooij, Johan M. M. van

doi:10.1007/978-3-642-13073-1_8

Cited by 7 publications

(3 citation statements)

References 20 publications

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“…Table 1 shows the evolution of P and U through the five iterations in the example. Finally, the domatic partition is {(1, 4, 6), (5,7,8,10), (2,3,9)}. This is illustrated in Figure 5.…”

Section: Block Decomposition Algorithmmentioning

confidence: 99%

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The Domatic Partition Problem in Separable Graphs

Landete

Sainz-Pardo

2022

Mathematics

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The domatic partition problem consists of partitioning a given graph into a maximum number of disjoint dominating sets. This problem is related with the domatic number problem, which consists of quantifying this maximum number of disjoint dominating sets. Both problems were proved to be NP-complete. In this paper, we present a decomposition algorithm for finding a domatic partition on separable graphs, that is, on graphs with blocks, and as a consequence, its domatic number, highly reducing the computational complexity. Computational results illustrate the benefits of the block decomposition algorithm.

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“…Table 1 shows the evolution of P and U through the five iterations in the example. Finally, the domatic partition is {(1, 4, 6), (5,7,8,10), (2,3,9)}. This is illustrated in Figure 5.…”

Section: Block Decomposition Algorithmmentioning

confidence: 99%

“…Finally, the Ref. [7] introduced an algorithm that combines both the measure and conquer and the inclusion-exclusion techniques for calculating the domatic number in O(2.7139 n ) time and polynomial space. This algorithm is based on another algorithm for counting the dominating sets in O(1.5673 n ) time formulated in the same paper.…”

Section: Introductionmentioning

confidence: 99%

The Domatic Partition Problem in Separable Graphs

Landete

Sainz-Pardo

2022

Mathematics

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“…Nederlof [44] further developed inclusion-exclusion techniques to derive a number of polynomial space algorithms. Additionally, the approach based on a combination of branching and inclusion-exclusion is developed in [45,50,48,47]. For the recent progress on the algorithmic uses of inclusion-exclusion, please refer to the survey by Husfeldt [34].…”

Section: Notesmentioning

confidence: 99%

Faster and Space Efficient Exact Exponential Algorithms: Combinatorial and Algebraic Approaches

Wang

Hua

et al. 2013

Handbook of Combinatorial Optimization

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Abstract. Exponential algorithms, whose time complexity is O(c n ) for some constant c > 1, are inevitable when exactly solving NP-complete problems unless P = NP. This chapter presents recently emerged combinatorial and algebraic techniques for designing exact exponential time algorithms. The discussed techniques can be used either to derive faster exact exponential algorithms, or to significantly reduce the space requirements while without increasing the running time. For illustration, exact algorithms arising from the use of these techniques for some optimization and counting problems are given.

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