Some simplified NP-complete problems

Garey, M. R.; Johnson, D. S.; Stockmeyer, Larry J.

doi:10.1145/800119.803884

Cited by 458 publications

(265 citation statements)

References 16 publications

Supporting

Mentioning

263

Contrasting

Unclassified

Order By: Relevance

“…In fact, edge deletion problems in general tend to be NP-complete. For example, edge deletion to a cluster graph [42], bipartite graph [19], threshold graph [38], and interval graph [21] are all NP-complete. A well-studied edge insertion problem is the sandwich problem, which has applications in DNA mapping and parallel processing [23].…”

Section: Graph Editingmentioning

confidence: 99%

See 1 more Smart Citation

Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

Nishimura

Subramanya

2017

Combinatorial Optimization and Applications

View full text Add to dashboard Cite

Section: Graph Editingmentioning

confidence: 99%

“…First, to show that GEN is NP-hard, we reduce Vertex-Cover, which is known to be NP-hard [19], to GEN. Let (G, k) be an instance of Vertex-Cover. We claim that (G, k) is a yes-instance if and only if (G, T E , k) is a yes-instance of GEN, where T E is the empty Young tableau.…”

Section: Lemma 45 Given An Edit Pair (X Y ) That Fits a Graph G Thmentioning

confidence: 99%

Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

Nishimura

Subramanya

2017

Combinatorial Optimization and Applications

View full text Add to dashboard Cite

“…In 1977, Garey and Johnson published the first proof of the NPhardness of this problem [9]. They also needed to employ the result of Garey, Johnson and Stockmeyer that the planar version of Vertex Cover still remains NP-hard, which was published one year earlier [10]. The line of reductions in [9] is the following:…”

Section: The Reduction Of Garey and Johnsonmentioning

confidence: 99%

On the Hardness of Range Assignment Problems

Fuchs

2006

Lecture Notes in Computer Science

View full text Add to dashboard Cite

We investigate the computational hardness of the Connectivity, the Strong Connectivity and the Broadcast type of Range Assignment Problems in R 2 and R 3 . We present new reductions for the Connectivity problem, which are easily adapted to suit the other two problems. All reductions are considerably simpler than the technically quite involved ones used in earlier works on these problems. Using our constructions, we can for the first time prove NP-hardness of these problems for all real distance-power gradients α > 0 (resp. α > 1 for Broadcast) in 2-d, and give improved lower bounds on the approximation ratios of all three problems in 3-d for all α > 1. In particular, we derive the overall first APX-hardness proof for Broadcast. This was an open problem posed in earlier work in this area, as was the question whether (Strong) Connectivity remains NP-hard for α = 1. Additionally, we give the first hardness results for so-called well-spread instances.

show abstract

“…The known NP-complete problem of determining whether an undirected graph is three colorable [Cormen et al 1990;Garey et al 1976] is reduced to an instance of this satisfiability problem.…”

Section: The General Satisfiability Problemmentioning

confidence: 99%

Solving satisfiability and implication problems in database systems

Guo

Sun

Weiss³

1996

ACM Trans. Database Syst.

View full text Add to dashboard Cite

Satisfiability, implication, and equivalence problems involving conjunctive inequalities are important and widely encountered database problems that need to be efficiently and effectively processed. In this article we consider two popular types of arithmetic inequalities, (X op Y) and (X op C), where X and Y are attributes, C is a constant of the domain or X, and op ʦ {Ͻ, Յ, ϭ, , Ͼ, Ն}. These inequalities are most frequently used in a database system, inasmuch as the former type of inequality represents a -join, and the latter is a selection. We study the satisfiability and implication problems under the integer domain and the real domain, as well as under two different operator sets ({Ͻ, Յ, ϭ, Ն, Ͼ} and {Ͻ, Յ, ϭ, , Ն, Ͼ}). Our results show that solutions under different domains and/or different operator sets are quite different. Out of these eight cases, excluding two cases that had been shown to be NP-hard, we either report the first necessary and sufficient conditions for these problems as well as their efficient algorithms with complexity analysis (for four cases), or provide an improved algorithm (for two cases). These iff conditions and algorithms are essential to database designers, practitioners, and researchers. These algorithms have been implemented and an experimental study comparing the proposed algorithms and those previously known is conducted. Our experiments show that the proposed algorithms are more efficient than previously known algorithms even for small input.

show abstract

Some simplified NP-complete problems

Cited by 458 publications

References 16 publications

Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

On the Hardness of Range Assignment Problems

Solving satisfiability and implication problems in database systems

Contact Info

Product

Resources

About