Cloud radio access networks (C-RANs) are proposed as promising architecture to improve the capacity and enhance the coverage of mobile communication systems. In this letter, we study the baseband unit (BBU) pools plan...
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Cloud radio access networks (C-RANs) are proposed as promising architecture to improve the capacity and enhance the coverage of mobile communication systems. In this letter, we study the baseband unit (BBU) pools planning problem in the C-RAN, where we try to minimize the total deployment cost while satisfying the traffic demands of remote radio heads connected to the BBU pools, the processing capacity of each BBU pool, and the latency requirements of the C-RAN. Our problem formulation leads a mixed integer linear programming problem that is NP-hard. We introduce an approximation algorithm to address it efficiently. Numerical results show that our proposed algorithm performs much better than other heuristic ones that are popular to deal with such kind of optimization tasks. Moreover, our proposal also yields a performance guaranteed scheme for the BBU pools planning problem in the C-RAN.
We consider the problem of packing squares into bins which are unit squares, where the goal is to minimize the number of bins used. We present an algorithm for this problem with an absolute worst-case ratio of 2, whic...
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We consider the problem of packing squares into bins which are unit squares, where the goal is to minimize the number of bins used. We present an algorithm for this problem with an absolute worst-case ratio of 2, which is optimal provided P not equal NP. (C) 2004 Elsevier B.V. All rights reserved.
We study the NP-hard problem of labeling points with maximum-radius circle pairs: given n point sites in the plane, find a placement for 2n interior-disjoint uniform circles, such that each site touches two circles an...
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We study the NP-hard problem of labeling points with maximum-radius circle pairs: given n point sites in the plane, find a placement for 2n interior-disjoint uniform circles, such that each site touches two circles and the circle radius is maximized. We present a new approximation algorithm for this problem that runs in O(n log n + n log epsilon\1) time and O(n) space and achieves an approximation factor of (2 + root 3 + 2 root 4 + root 3)/(4 + root 3) + epsilon (approximate to 1.486 + epsilon), which improves the previous best bound of 1.491 + epsilon. (c) 2006 Elsevier B.V. All rights reserved.
In the hybrid flow shop, jobs are subjected to process through stages in series as in the classical flow shop, while each stage contains one or more identical machines. This paper mainly studies the scheduling problem...
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In the hybrid flow shop, jobs are subjected to process through stages in series as in the classical flow shop, while each stage contains one or more identical machines. This paper mainly studies the scheduling problem in the two-stage hybrid flow shop, namely the proportionate scheduling. In such problem, it is assumed that each job has the same processing time in different stages. The objective of minimizing the makespan is considered. If there are two machines in the first stage and m machines in the second, then an approximation algorithm with worst case ratio no more than 3/2 is provided. If each stage consists of only two machines, we show that the tight bound of our algorithm can be reduced to 4/3. (C) 2014 Elsevier B.V. All rights reserved.
The traveling salesman problem (TSP) is one of the classic research topics in the field of operations research, graph theory and computer science. In this paper, we propose a generalized model of traveling salesman pr...
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The traveling salesman problem (TSP) is one of the classic research topics in the field of operations research, graph theory and computer science. In this paper, we propose a generalized model of traveling salesman problem, denoted by generalized traveling salesman path problem. Let G = (V, E, c) be a weighted complete graph, in which c is a nonnegative metric cost function on edge set E, i.e., c : E -> R+. The traveling salesman path problem aims to find a Hamiltonian path in G with minimum cost. Compared to the traveling salesman path problem, we are given extra vertex subset V ' and edge subset E' in the problem proposed in this paper;its goal is to construct a path which traverses all the edges in E' while only needs to visit each vertex in V ' exactly once. Based on integer programming, we give a mathematical model of the problem, and design a 1+root 5 2 -approximation algorithm for the problem by combining linear programming rounding strategy and a special graph structure.
Given a hypergraph with nonnegative costs on hyperedges, and a weakly supermodular function r: 2(V) --> Z(+), where V is the vertex set, we consider the problem of finding a minimum cost subset of hyperedges such t...
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Given a hypergraph with nonnegative costs on hyperedges, and a weakly supermodular function r: 2(V) --> Z(+), where V is the vertex set, we consider the problem of finding a minimum cost subset of hyperedges such that for every set S subset of or equal to V, there are at least r(S) hyperedges that have at least one but no all endpoints in S. This problem captures a hypergraph generalization of the survivable network design problem (SNDP), and also the element connectivity problem (ECP). We present a primal-dual algorithm with a performance guarantee of d(max)(+) H(r(max)), where d(max)(+) is the maximum degree of hyperedges of positive costs, r(max) =max(S) r(S), and H(k)= 1 + 1/2 +(...)+ 1/k. In particular, our result contains a 2H(r(max))-approximation algorithm for ECP, which gives an independent and complete proof for the result first obtained by Jain et al. (Proceedings of the SODA, 1999, p. 484-489). (C) 2002 Elsevier Science B.V. All rights reserved.
We improve the approximation ratio for MAXIMUM WEIGHT SERIES-PARALLEL SUBGRAPH from 1 / 2 to 1 / 2 + 1 / 60. (c) 2023 Elsevier B.V. All rights reserved.
We improve the approximation ratio for MAXIMUM WEIGHT SERIES-PARALLEL SUBGRAPH from 1 / 2 to 1 / 2 + 1 / 60. (c) 2023 Elsevier B.V. All rights reserved.
We devise a constant-factor approximation algorithm for the maximization version of the edge-disjoint paths problem if the supply graph together with the demand edges forms a planar graph. By planar duality, this is e...
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We devise a constant-factor approximation algorithm for the maximization version of the edge-disjoint paths problem if the supply graph together with the demand edges forms a planar graph. By planar duality, this is equivalent to packing cuts in a planar graph such that each cut contains exactly one demand edge. We also show that the natural linear programming relaxations have constant integrality gap, yielding an approximate max-multiflow min-multicut theorem.
Emerging applications with low-latency requirements such as real-time analytics, immersive media applications, and intelligent virtual assistants have rendered Edge Computing as a critical computing infrastructure. Ex...
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Emerging applications with low-latency requirements such as real-time analytics, immersive media applications, and intelligent virtual assistants have rendered Edge Computing as a critical computing infrastructure. Existing studies have explored the cloudlet placement problem in a homogeneous scenario with different goals such as latency minimization, load balancing, energy efficiency, and placement cost minimization. However, placing cloudlets in a highly heterogeneous deployment scenario considering the next-generation 5G networks and IoT applications is still an open challenge. The novel requirements of these applications indicate that there is still a gap in ensuring low-latency service guarantees when deploying cloudlets. Furthermore, deploying cloudlets in a cost-effective manner and ensuring full coverage for all users in edge computing are other critical conflicting issues. In this article, we address these issues by designing a bifactor approximation algorithm to solve the heterogeneous cloudlet placement problem to guarantee a bounded latency and placement cost, while fully mapping user applications to appropriate cloudlets. We first formulate the problem as a multi-objective integer programming model and show that it is a computationally NP-hard problem. We then propose a bifactor approximation algorithm, ACP, to tackle its intractability. We investigate the effectiveness of ACP by performing extensive theoretical analysis and experiments on multiple deployment scenarios based on New York City OpenData. We prove that ACP provides a (2,4)-approximation ratio for the latency and the placement cost. The experimental results show that ACP obtains near-optimal results in a polynomial running time making it suitable for both short-term and long-term cloudlet placement in heterogeneous deployment scenarios.
Kou, Markowsy, and Berman (1981) described a procedure for finding a Steiner tree for a connected, undirected distance graph with a specified subset of the set of vertices. A new implementation of that 1981 algorithm...
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Kou, Markowsy, and Berman (1981) described a procedure for finding a Steiner tree for a connected, undirected distance graph with a specified subset of the set of vertices. A new implementation of that 1981 algorithm is described. Using the new implementation, it is possible to find a Steiner tree whose total distance of all edges is at most 2 times one minus (one divided by the minimum number of leaves greater than the total distance of all edges of a Steiner minimal tree). The solution is both faster and simpler than previous solutions to the problem since it reduces the question being considered to a shortest path and a minimum spanning tree calculation. The algorithm: 1. constructs the complete distance graph for the connected undirected distance graph (G), 2. finds a minimum spanning tree for the complete distance graph, 3. constructs a subgraph of G, 4. finds a minimum spanning tree of the subgraph of G, and 5. constructs a Steiner tree from the minimum spanning tree so no leaves in the Steiner tree are Steiner vertices.
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