Graph coloring with cardinality constraints on the neighborhoods

Costa, Marie-Christine; Werra, Dominique de; Picouleau, Christophe; Ries, Bernard

doi:10.1016/j.disopt.2009.04.005

Cited by 9 publications

(5 citation statements)

References 22 publications

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“…The decisional version of λ 2,1 (G) for bipartite graphs had been proved to be NP-complete in [1]. It was also proved in [6] that the L(1, 1)-labeling problem for bipartite graphs with maximum degree 3 and four labels is NP-complete. The approximating algorithms for L( j, k)-labelings of bipartite graphs were investigated in [2,13].…”

Section: λ 21 (G) and λ 31 (G) For Bipartite Graphsmentioning

confidence: 96%

Group path covering and distance two labeling of graphs

Wang

Lin

2011

Information Processing Letters

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Section: λ 21 (G) and λ 31 (G) For Bipartite Graphsmentioning

confidence: 96%

Group path covering and distance two labeling of graphs

Wang

Lin

2011

Information Processing Letters

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“…L(1, 1)-labelling. The decision version of the L(1, 1)-labelling problem is NP-complete even for 3-regular bipartite graphs using 4 colors [47]. In [6] it is proven that the L(1, 1)-labelling problem on bipartite graphs is hard to approximate within a factor of n 1/2−ǫ , for any ǫ > 0, unless NP-problems have randomized polynomial time algorithms.…”

Section: Bipartite Graphsmentioning

confidence: 99%

The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

Calamoneri

2011

The Computer Journal

160

104

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Given any fixed nonnegative integer values h and k, the L(h, k)labelling problem consists in an assignment of nonnegative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with minimum span. The L(h, k)-labelling problem has been intensively studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach. It is an update of a previous survey written by the same author.

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“…For example, certain properties in cryptography are more conveniently described with XOR [Bogdanov et al, 2011]. In addition, cardinality constraints help formulate problems in graph coloring [Costa et al, 2009], and hybrid constraints have also been used for maximum-likelihood decoding [Feldman et al, 2005].…”

Section: Introductionmentioning

confidence: 99%

DPO: Dynamic-Programming Optimization on Hybrid Constraints

Phan¹,

Vardi²

2022

Preprint

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In Bayesian inference, the most probable explanation (MPE) problem requests a variable instantiation with the highest probability given some evidence. Since a Bayesian network can be encoded as a literal-weighted CNF formula ϕ, we study Boolean MPE, a more general problem that requests a model τ of ϕ with the highest weight, where the weight of τ is the product of weights of literals satisfied by τ . It is known that Boolean MPE can be solved via reduction to (weighted partial) MaxSAT. Recent work proposed DPMC, a dynamic-programming model counter that leverages graph-decomposition techniques to construct project-join trees. A project-join tree is an execution plan that specifies how to conjoin clauses and project out variables. We build on DPMC and introduce DPO, a dynamic-programming optimizer that exactly solves Boolean MPE. By using algebraic decision diagrams (ADDs) to represent pseudo-Boolean (PB) functions, DPO is able to handle disjunctive clauses as well as XOR clauses. (Cardinality constraints and PB constraints may also be compactly represented by ADDs, so one can further extend DPO's support for hybrid inputs.) To test the competitiveness of DPO, we generate random XOR-CNF formulas. On these hybrid benchmarks, DPO significantly outperforms MaxHS, UWrMaxSat, and GaussMaxHS, which are state-of-the-art exact solvers for MaxSAT.

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Graph coloring with cardinality constraints on the neighborhoods

Cited by 9 publications

References 22 publications

Group path covering and distance two labeling of graphs

Group path covering and distance two labeling of graphs

The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

DPO: Dynamic-Programming Optimization on Hybrid Constraints

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