An NP-complete number-theoretic problem

Gurari, Eitan M.; Ibarra, Óscar H.

doi:10.1145/800133.804349

Cited by 9 publications

(3 citation statements)

References 10 publications

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“…Constraints (11) represent that decision variables are binary. Therefore, the ESDP instance is binary linear programming which has been proven as NP-complete [15]. Thus, ESDP is NP-complete.…”

Section: Problem Statementmentioning

confidence: 99%

A Hybrid metaheuristic Algorithm for Edge Site Deployment with User Coverage Maximization and Cost Minimization

Xing,

Song,

Wang

2023

IJACSA

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Recent years, edge computing has been getting increased attention due to its ultra-low delay service deliveries. Plenty of works have focused on the performance improvement of edge computing by e.g., edge server deployment, edge caching, and task offloading. While, there is a lack of work on improving the investment cost for building or upgrading the edge site deployment by making a decision on which places edge sites are deployed. In this paper, we focus on the edge site deployment problem (ESDP) to maximize user coverage with fewest edge sites. We first formulate ESDP into a binary nonlinear programming with two optimization objectives of user coverage maximization and edge site minimization, and prove that ESDP is NP-complete. Then, we propose a hybrid meta-heuristic algorithm to solve ESDP with polynomial time complexity, which combining the crossover and mutation operators of genetic algorithm with selfand social-cognition of particle swarm optimization. At last, we conduct extensive simulated experiment based on a real data set to evaluate the performance of our proposed algorithm. The results show that our algorithm achieves 100% user coverage with much fewer edge sites than other seven meta-heuristic algorithms, and has a good scalability.

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Section: Problem Statementmentioning

confidence: 99%

A Hybrid metaheuristic Algorithm for Edge Site Deployment with User Coverage Maximization and Cost Minimization

Xing,

Song,

Wang

2023

IJACSA

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“…The proof essentially shows that existence of such a pseudo-run amounts to solving an inequation system and by using [8], small solutions exist, whence the existence of a short i-B-bounded pseudo-run (the same technique is used in forthcoming Lemma 4.2). The idea of using small solutions of inequation system to solve problems on counter systems dates back from [45,23] and nowadays, this is a standard proof technique, see e.g. [15].…”

Section: Motivations For Approximating Propertiesmentioning

confidence: 99%

On Selective Unboundedness of VASS

Demri

2010

Electron. Proc. Theor. Comput. Sci.

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Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, counter values, run lengths). Some of these features can be checked in exponential space by using Rackoff's proof or its variants, combined with Savitch's Theorem. However, the question is still open for many others, e.g., regularity detection problem and reversal-boundedness detection problem. In the paper, we introduce the class of generalized unboundedness properties that can be verified in exponential space by extending Rackoff's technique, sometimes in an unorthodox way. We obtain new optimal upper bounds, for example for place boundedness problem, reversal-boundedness detection (several variants are present in the paper), strong promptness detection problem and regularity detection. Our analysis is sufficiently refined so as to obtain a polynomial-space bound when the dimension is fixed.

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“…Non-linear Diophantine constraints have been widely investigated in mathematical optimisation and automated reasoning. Despite the number of applications of prequadratic [1,12,20,45,50] and more general constraints [16,21,23,25,30,49,52] there exist few classes in the literature with low complexity bounds making them suitable for integration in satisfiability modulo theory solvers [6,7,9,11,14,46]. In this work, we prove an optimal bound for a subfamily of prequadratic Diophantine constraints.…”

Section: Discussionmentioning

confidence: 97%

On the Complexity of Convex and Reverse Convex Prequadratic Constraints

Raya¹,

Hamza²,

Kunčak³

EPiC Series in Computing

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Motivated by satisfiability of constraints with function symbols, we consider numerical inequalities on non-negative integers. The constraints we address are a conjunction of a linear system Ax = b and an arbitrary number of (reverse) convex constraints of the form xi ≥ xdj (xi ≤ xdj ). We show that the satisfiability of these constraints is NP-complete even if the solution to the linear part is given explicitly. As a consequence, we obtain NP- completeness for an extension of certain quantifier-free constraints on sets with cardinalities and function images.

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An NP-complete number-theoretic problem

Abstract: Systems of nonlinear equations of the form D:

Cited by 9 publications

References 10 publications

A Hybrid metaheuristic Algorithm for Edge Site Deployment with User Coverage Maximization and Cost Minimization

A Hybrid metaheuristic Algorithm for Edge Site Deployment with User Coverage Maximization and Cost Minimization

On Selective Unboundedness of VASS

On the Complexity of Convex and Reverse Convex Prequadratic Constraints

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