Given a graph G, the minimum Connected-k-Subgraph Cover problem (MinCkSC) is to find a minimum vertex subset C of G such that every connected subgraph of G on k vertices has at least one vertex in C. If furthermore th...
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Given a graph G, the minimum Connected-k-Subgraph Cover problem (MinCkSC) is to find a minimum vertex subset C of G such that every connected subgraph of G on k vertices has at least one vertex in C. If furthermore the subgraph of G induced by C is connected, then the problem is denoted as MinCkSC(con). In this paper, we first present a PTAS for MinCkSC on an H-minor-free graph, where H is a graph with a constant number of vertices. Then, we design an O((omega + 1)(2(k - 1)(omega + 2))(3 omega +3))|V|-time FPT algorithm for MinCkSC(con) on a graph with treewidth omega, based on which we further design an O(2(O(root tlog t)|V|O(1))) time subexponential FPT algorithm for MinCkSC(con) on an H-minor-free graph, where t is an upper bound of solution size.
A special case of the bottleneck Steiner tree problem in the Euclidean plane was considered in this paper. The problem has applications in the design of wireless communication networks, multifacility location, VLSI ro...
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A special case of the bottleneck Steiner tree problem in the Euclidean plane was considered in this paper. The problem has applications in the design of wireless communication networks, multifacility location, VLSI routing and network routing. For the special case which requires that there should be no edge connecting any two Steiner points in the optimal solution, a 3-restricted Steiner tree can be found indicating the existence of the performance ratio root2. In this paper, the special case of the problem is proved to be NP-hard and cannot be approximated within ratio root2. First a simple polynomial time approximation algorithm with performance ratio root3 is presented. Then based on this algorithm and the existence of the 3-restricted Steiner tree, a polynomial time approximation algorithm with performance ratio-root2 + epsilon is proposed, for any epsilon > 0.
We present a new polynomial-time heuristic algorithm for finding a solution to the Travelling Salesman Problem (TSP) for any complete and edge-weighted graph K n , with a set of vertices V and a set of edges E where |...
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We present a new polynomial-time heuristic algorithm for finding a solution to the Travelling Salesman Problem (TSP) for any complete and edge-weighted graph K n , with a set of vertices V and a set of edges E where | V | = n . In a few words, this method is based on the idea of linking the elements of V progressively, one by one, in such a way that the vertex selection which produces fewest disturbances to the other vertices not yet connected, will be selected as the next vertex to join to the subset of already connected vertices. When the cost of the result is compared to the cost of the best circuit, it appears that a good sub-solution is obtained in most of the cases tested. Moreover, comparison tests made between the heuristic introduced and the well-known Quick method, produce a better behaviour, for almost every case, in the first approach.
This paper presents a three-dimensional (3D) massive multiple-input and multiple-output (MIMO) antenna array model, which includes the spherical array assumption and geometric properties for future fifth generation (5...
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This paper presents a three-dimensional (3D) massive multiple-input and multiple-output (MIMO) antenna array model, which includes the spherical array assumption and geometric properties for future fifth generation (5G) wireless communications. A parametric approximation algorithm is developed for estimating the spatial fading correlations (SFCs) and channel capacities of the 3D massive MIMO antenna array systems under different power angular spectrum (PAS). The relationship between correlation with the spacing of antenna arrays and angular parameters was classified. The results show that the simulation values of the approximate method fit the theoretical calculation very well, thereby validating the feasibility of the proposed 3D large-scale massive MIMO model.
In a wireless sensor network, the virtual backbone plays an important role. Due to accidental damage or energy depletion, it is desirable that the virtual backbone is fault-tolerant. A fault-tolerant virtual backbone ...
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In a wireless sensor network, the virtual backbone plays an important role. Due to accidental damage or energy depletion, it is desirable that the virtual backbone is fault-tolerant. A fault-tolerant virtual backbone can be modeled as a k-connected m-fold dominating set ((k, m)-CDS for short). In this paper, we present a constant approximation algorithm for the minimum weight (k, m)-CDS problem in unit disk graphs under the assumption that k and m are two fixed constants with m >= k. Prior to this paper, constant approximation algorithms are known for k = 1 with weight and 2 <= k <= 3 without weight. Our result is the first constant approximation algorithm for the (k, m)-CDS problem with general k, m and with weight. The performance ratio is (alpha+5 rho) for k >= 3 and (alpha+2.5 rho) for k = 2, where a is the performance ratio for the minimum weight m-fold dominating set problem and. is the performance ratio for the subset k-connected subgraph problem (both problems are known to have constant performance ratios).
Given a graph G = (V, E) and a function r : V -> {0, 1, 2}, a node v is an element of V is said to be Roman dominated if r(v) = 1 or there exists a node u is an element of N-G[v] such that r(u) = 2, where N-G[v] is...
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Given a graph G = (V, E) and a function r : V -> {0, 1, 2}, a node v is an element of V is said to be Roman dominated if r(v) = 1 or there exists a node u is an element of N-G[v] such that r(u) = 2, where N-G[v] is the closed neighbor set of v in G. For i is an element of {0, 1, 2}, denote V-r(i) as the set of nodes with value i under function r. The cost of r is defined to be c(r) = vertical bar V-r(1)vertical bar + 2 vertical bar V-r(2)vertical bar. Given a positive integer Q <= vertical bar V vertical bar, the minimum partial connected Roman dominating set (MinPCRDS) problem is to compute aminimum cost function r such that at least Q nodes in G are Roman dominated and the subgraph of G induced by V-r(1) boolean OR V-r(2) is connected. In this paper, we give a (3 ln vertical bar V vertical bar + 9)-approximation algorithm for the MinPCRDS problem.
In a sweep cover problem, positions of interest (PoIs) are required to be visited periodically by mobile sensors. In this paper, we propose a new sweep cover problem: the prize -collecting sweep cover problem (PCSC), ...
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In a sweep cover problem, positions of interest (PoIs) are required to be visited periodically by mobile sensors. In this paper, we propose a new sweep cover problem: the prize -collecting sweep cover problem (PCSC), in which penalty is incurred by those PoIs which are not sweep-covered, and the goal is to minimize the covering cost plus the penalty. Assuming that every mobile sensor has to be linked to some base station, and the number of base stations is upper bounded by a constant, we present a 5-LMP (Lagrangian Multiplier Preserving) algorithm. As a step stone, we propose the prize-collecting forest with k components problem (PCFk), which might be interesting in its own sense, and presented a 2-LMP for rooted PCFk. (C) 2022 Elsevier B.V. All rights reserved.
Facility location problem is one of the most classical NP-hard problems in combinatorial optimization. In the metric facility location problem (MFLP), we are given a set of facilities, a set of clients and the metric ...
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Facility location problem is one of the most classical NP-hard problems in combinatorial optimization. In the metric facility location problem (MFLP), we are given a set of facilities, a set of clients and the metric distances between facilities and clients. In this paper, we consider the squared metric facility location problem (SMFLP) with nonuniform capacities, where each facility has a nonuniform capacity to serve a limited amount of client demands, and the distances between facilities and clients are no longer metric but squared metric. Fernandes et al. (2015) analyze the LP-based algorithms for the MFLP when they are applied to the SMFLP and achieve constant approximation ratios. In this paper, we do the same thing on local search algorithm, one of the most powerful techniques for MFLP with nonuniform capacities. Particularly, we propose the first constant approximation algorithm with approximation ratio 13 + epsilon for the SMFLP with nonuniform capacities. (C) 2019 Elsevier B.V. All rights reserved.
In a minimum partial set multi-cover problem (MinPSMC), given an element set X, a collection of subsets S subset of 2(X), a cost c(S) on each set S is an element of S, a covering requirement r(x) for each element x is...
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In a minimum partial set multi-cover problem (MinPSMC), given an element set X, a collection of subsets S subset of 2(X), a cost c(S) on each set S is an element of S, a covering requirement r(x) for each element x is an element of X, and an integer k, the goal is to find a sub-collection F subset of S to fully cover at least k elements such that the cost of F is as small as possible, where element x is fully covered by F if it belongs to at least r(x) sets of F. Recently, it was proved that MinPSMC is at least as hard as the densest k-subgraph problem. The question is: how about the problem in some geometric settings? In this paper, we consider the MinPSMC problem in which X is a set of points on the plane and S is a set of unit squares (MinPSMC-US). Under the assumption that r(x) = f(x) for every x is an element of X, where f(x) = vertical bar{S is an element of S : x is an element of S}vertical bar is the number of sets containing element x, we design an approximation algorithm achieving approximation ratio (1 + epsilon) for MinPSMC-US.
In this paper, we consider a variant of the classical uncapacitated facility location problem, so-called squared metric two-stage stochastic facility location problem (SM-2-SFLP) which can treat the uncertainty of the...
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In this paper, we consider a variant of the classical uncapacitated facility location problem, so-called squared metric two-stage stochastic facility location problem (SM-2-SFLP) which can treat the uncertainty of the set of clients and facility costs. We assume that the connection cost is squared metric, a variant of the metric case which is widely researched. We give a new 0-1 integer linear programming for SM-2-SFLP. Based on the new formulation, we apply two known algorithms to SM-2-SFLP, and analyze the approximation ratio and per-scenario bound respectively.
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