In this paper, we study the minimum (connected) k-bounded-degree node deletion problem (Min(C)kBDND). For a connected graph G, a constant k and a weight function w : V -> R+, a vertex set C subset of V (G) is a kBD...
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In this paper, we study the minimum (connected) k-bounded-degree node deletion problem (Min(C)kBDND). For a connected graph G, a constant k and a weight function w : V -> R+, a vertex set C subset of V (G) is a kBDND-set if the maximum degree of graph G - C is at most k. If furthermore, the subgraph of G induced by C is connected, then C is a CkBDND-set. The goal of MinWkBDND (resp. MinWCkBDND) is to find a kBDND-set (resp. CkBDND-set) with the minimum weight. In this paper, we focus on their cardinality versions with w(v) equivalent to 1, v is an element of V, which are denoted as MinkBDND and MinCkBDND. This paper presents a (1 + epsilon) and a 3.76-approximation algorithm for MinkBDND and MinCkBDND on unit disk graphs, respectively, where 0 < epsilon <1 is an arbitrary constant. (C) 2020 Published by Elsevier B.V.
We consider the problem of partitioning a finite sequence of Euclidean points into a given number of clusters (subsequences) using the criterion of the minimal sum (over all clusters) of intercluster sums of squared d...
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We consider the problem of partitioning a finite sequence of Euclidean points into a given number of clusters (subsequences) using the criterion of the minimal sum (over all clusters) of intercluster sums of squared distances from the elements of the clusters to their centers. It is assumed that the center of one of the desired clusters is at the origin, while the center of each of the other clusters is unknown and determined as the mean value over all elements in this cluster. Additionally, the partition obeys two structural constraints on the indices of sequence elements contained in the clusters with unknown centers: (1) the concatenation of the indices of elements in these clusters is an increasing sequence, and (2) the difference between an index and the preceding one is bounded above and below by prescribed constants. It is shown that this problem is strongly NP-hard. A 2-approximation algorithm is constructed that is polynomial-time for a fixed number of clusters.
The problem of diagnostic test scheduling (DTS) is to assign to each edge e of a diagnostic graph G a time interval of length l(e) so that intervals corresponding to edges at any given vertex do not overlap and the ov...
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The problem of diagnostic test scheduling (DTS) is to assign to each edge e of a diagnostic graph G a time interval of length l(e) so that intervals corresponding to edges at any given vertex do not overlap and the overall finishing time is minimum. In this correspondence we show that the DTS problem is NP-complete. Then we present a longest, first sequential scheduling algorithm which runs in worst case time O(dm log n) and uses O(m) space to produce a solution of length less than four times optimal. Then we show that the general performance bound can be strengthened to 3 * OPT(G) for low-degree graphs and to 2 ·OPT(G) in some special cases of binomial diagnostic graphs.
In this paper, we study the uncapacitated facility location problem with service installation costs depending on the type of service required. We propose a polynomial-time approximation algorithm with approximation ra...
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In this paper, we study the uncapacitated facility location problem with service installation costs depending on the type of service required. We propose a polynomial-time approximation algorithm with approximation ratio 1.808 which improves the previous approximation ratio of 2.391 of Shmoys, Swamy, and Levi. (c) 2007 Elsevier B.V. All rights reserved.
Using outward rotations, we obtain an approximation algorithm for Max-Bisection problem, i.e., partitioning the vertices of an undirected graph into two blocks of equal cardinality so as to maximize the weights of cro...
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Using outward rotations, we obtain an approximation algorithm for Max-Bisection problem, i.e., partitioning the vertices of an undirected graph into two blocks of equal cardinality so as to maximize the weights of crossing edges. In many interesting cases, the algorithm performs better than the algorithms of Ye and of Halperin and Zwick. The main tool used to obtain this result is semidefinite programming.
In this paper we study the scheduling of a given set of jobs on several identical parallel machines tended by a common server. Each job must be processed on one of the machines. Prior to processing, the server has to ...
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In this paper we study the scheduling of a given set of jobs on several identical parallel machines tended by a common server. Each job must be processed on one of the machines. Prior to processing, the server has to set up the relevant machine. The objective is to schedule the jobs so as to minimize the total weighted job completion times. We provide an approximation algorithm to tackle this intractable problem and analyze the worst-case performance of the algorithm for the general, as well as a special, case of the problem.
We study an infinite-dimensional operator equation XL - BX = C in a separable Hilbert space. The equation arises in the stabilization study of general linear parabolic systems, where the operators L, B, and C are coef...
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We study an infinite-dimensional operator equation XL - BX = C in a separable Hilbert space. The equation arises in the stabilization study of general linear parabolic systems, where the operators L, B, and C are coefficient operators describing a Feedback control system. The solution to the stabilization naturally leads to an approximation problem of the operator equation. In this paper we propose a concrete algorithm for the approximation with the prescribed convergence rate when the closed operator L is self-adjoint or more generally a spectral operator with compact resolvent.
To eliminate the routing load unbalance among sensor nodes, one approach is to deploy a small number of powerful relay nodes acting as routing nodes in wireless sensor networks, the major optimization objective of whi...
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To eliminate the routing load unbalance among sensor nodes, one approach is to deploy a small number of powerful relay nodes acting as routing nodes in wireless sensor networks, the major optimization objective of which is to minimize the number of relay nodes required. In this paper, we prove that the relay node placement problem in a bounded plane is a P problem, but its computational complexity in general case is quite great. From the geometric cover feature of the relay node placement problem, an O(n2 log n) time greedy approximation algorithm is proposed, where n is the number of sensor nodes. Particularly, at each stage of this algorithm's iterative process, we first select a critical node from uncovered sensor nodes, and then determine the location of relay node based on the principle of preferring to cover the sensor node closer to the critical node, so as to prevent the emergence of isolated node. Experiment results indicate that our proposed algorithm can generate a near optimum feasible relay node deployment in a very short time, and it outperforms existing algorithms in terms of both the size of relay node deployment and the execution time.
In this work we design an approximation algorithm using neighbors, history and errors (NHE algorithm) to analyze and approximate the behavior of sensors readings after it fails. NHE algorithm computes and associates a...
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ISBN:
(纸本)9781424429165
In this work we design an approximation algorithm using neighbors, history and errors (NHE algorithm) to analyze and approximate the behavior of sensors readings after it fails. NHE algorithm computes and associates a specific equation to each sensor that has factors computed using neighbors, history data and the approximation error as a feedback factor. In some cases, it is difficult to reach each sensor to read its value either due to a connection problem or the sensor itself is down and not reachable. In those cases, NHE algorithm uses the evaluated equations to approximate this down sensor reading. The results of the experiments using this algorithm prove that it is powerful but with specific constraints.
In this paper, we investigate the min-max correlation clustering problem with outliers, which is a combination of the min-max correlation clustering problem with the robust clustering. We first prove that the problem ...
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ISBN:
(纸本)9783030926816;9783030926809
In this paper, we investigate the min-max correlation clustering problem with outliers, which is a combination of the min-max correlation clustering problem with the robust clustering. We first prove that the problem is NP-hard to obtain any finite approximation algorithm. Then we design an approximation algorithm based on LP-rounding technique and receive a bi-criteria guarantee.
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