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Designing wireless radio access networks for third generation cellular networks
 in Proc. IEEE INFOCOM
, 2005
"... Abstruct In third generation (3G) cellular networks, base stations ate connected to base station controllers by pointtopoint (usually TlIE1) links. However, today’s TllEl based hackhaul network is not a good match for next generation wireless networks because symmetric Tls is not an efficient way ..."
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Abstruct In third generation (3G) cellular networks, base stations ate connected to base station controllers by pointtopoint (usually TlIE1) links. However, today’s TllEl based hackhaul network is not a good match for next generation wireless networks because symmetric Tls is not an efficient way to carry bursty and asymmetric data traffic. In this paper, we propose designing an IEEE 802.16based wireless radio access network to carry the traffic from the base station to the radio network controller. 802.16 has several characteristics that make it a better match for 36 radio acres % networks including its support for Time Division Duplex mode that supports asymmetry eficiently. In this paper, we tackle the following question: given a layout of base stations and base station controllers, how do we design the topology of the 802.16 radio access network connecting the base stations to the base station controller that minimizes the number of 802.16 links used while meeting the expected demands of traffic frodto the base station?? We make three contributions: we first sbow that finding the optimal solution to the problem is NPhard, We then provide heuristics that perform close to the optimal solution. Finally, we address the reliability issue of failure of 802.16 links or nodes by designing algorithms to create topologies that can handle single failures effectively. I.
Survivable Network Design: The Capacitated Minimum Spanning Network Problem
 In Proc. 7th INFORMS Telecommunications Conf
, 2004
"... We are given an undirected graph G = (V; E) with positive weights on its vertices representing demands, and nonnegative costs on its edges. Also given are a capacity constraint k, and root vertex r 2 V . In this paper, we consider the capacitated minimum spanning network (CMSN) problem, which as ..."
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We are given an undirected graph G = (V; E) with positive weights on its vertices representing demands, and nonnegative costs on its edges. Also given are a capacity constraint k, and root vertex r 2 V . In this paper, we consider the capacitated minimum spanning network (CMSN) problem, which asks for a minimum cost spanning network such that the the removal of r and its incident edges breaks the network into a number of components (groups), each of which is 2edgeconnected with a total weight of at most k. We show that the CMSN problem is NPhard, and present a 4approximation algorithm for graphs satisfying triangle inequality. We also show how to obtain similar approximation results for a related 2vertexconnected CMSN problem.
Dynamic Capacitated Minimum Spanning Trees
 In Proc. 3rd Intl. Conf. on Networking (ICN
, 2004
"... Given a set of terminals, each associated with a positive number denoting the traffic to be routed to a central terminal (root), the Capacitated Minimum Spanning Tree (CMST) problem asks for a minimum spanning tree, spanning all terminals, such that the amount of traffic routed from a subtree, linke ..."
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Given a set of terminals, each associated with a positive number denoting the traffic to be routed to a central terminal (root), the Capacitated Minimum Spanning Tree (CMST) problem asks for a minimum spanning tree, spanning all terminals, such that the amount of traffic routed from a subtree, linked to the root by an edge, does not exceed the given capacity constraint k. The CMST problem is NPcomplete and has been extensively studied for the past 40 years. Current best heuristics, in terms of cost and computation time (O(n log n)), are due to Esau and Williams [1], and Jothi and Raghavachari [2].
Revisiting EsauWilliams' Algorithm: On the Design of Local Access Networks
 IN PROC. 7TH INFORMS TELECOMMUNICATIONS CONF
, 2004
"... Given a set of nodes, each associated with a positive number denoting the traffic to be routed to a central node (root), the capacitated minimum spanning tree (CMST) problem asks for a minimum spanning tree, spanning all nodes, such that the amount of traffic routed from a subtree, linked to the ..."
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Cited by 2 (2 self)
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Given a set of nodes, each associated with a positive number denoting the traffic to be routed to a central node (root), the capacitated minimum spanning tree (CMST) problem asks for a minimum spanning tree, spanning all nodes, such that the amount of traffic routed from a subtree, linked to the root by an edge, does not exceed the given capacity constraint k. The CMST problem is NPcomplete and has been extensively studied for the past 40 years. Over the last 4 decades, numerous heuristics have been proposed to overcome the exponential time complexity of exact algorithms for the CMST problem. A major problem with most of the proposed heuristics is that their worstcase runningtimes may be exponential. The most popular and efficient algorithm for the CMST problem is due to Esau and Williams (EW), presented in 1966, with running time O(n² log n). Almost all of the heuristics that have been proposed so far, use EW algorithm as a benchmark to compare their results. Any other heuristic that outperforms EW algorithm do so with an enormous increase in running time. In this paper, we present the an O(n² log n) algorithm that comprehensively outperforms the EW algorithm.
An exact algorithm for maximum lifetime data gathering tree without aggregation in wireless sensor networks
"... Abstract In wireless sensor networks, maximizing the lifetime of a data gathering tree without aggregation has been proved to be NPcomplete. In this paper, we prove that, unless P = NP, no polynomialtime algorithm can approximate the problem with a factor strictly greater than 2/3. The result even ..."
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Abstract In wireless sensor networks, maximizing the lifetime of a data gathering tree without aggregation has been proved to be NPcomplete. In this paper, we prove that, unless P = NP, no polynomialtime algorithm can approximate the problem with a factor strictly greater than 2/3. The result even holds in the special case where all sensors have the same initial energy. Existing works for the problem focus on approximation algorithms, but these algorithms only find suboptimal spanning trees and none of them can guarantee to find an optimal tree. We propose the first nontrivial exact algorithm to find an optimal spanning tree. Due to the NPhardness nature of the problem, this proposed algorithm runs in exponential time in the worst case, but the consumed time is much less than enumerating all spanning trees. This is done by several techniques for speeding up the search. Featured techniques include how to grow the initial spanning tree and how to divide the problem into subproblems. The algorithm can handle small networks and be used as a benchmark for evaluating approximation algorithms.
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"... • We present a K − 1 simple approximation algorithm, this algorithm is suitable for small values of K. • We also present a 6approximation algorithm which is suitable for all values of K. – For k = 2 we present a 10approximation algorithm, suitable for all values ..."
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• We present a K − 1 simple approximation algorithm, this algorithm is suitable for small values of K. • We also present a 6approximation algorithm which is suitable for all values of K. – For k = 2 we present a 10approximation algorithm, suitable for all values
Allocating Virtual and Physical Flows for Multiagent Teams in Mutable, Networked Environments
, 2012
"... The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Army Research Laboratory, the U.S. Government, the U.K. Ministry of Defence or the U.K. Government. Keywords: mu ..."
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The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the U.S. Army Research Laboratory, the U.S. Government, the U.K. Ministry of Defence or the U.K. Government. Keywords: multiple source network flow, partial centralization, network augmentation, The movement of information, agents, and resources is a crucial part of cooperative multiagent systems: decision makers must receive data in a timely manner to make good decisions, while agents and resources must be provided at appropriate locations for tasks to be completed. Flow allocation meets these conditions by computing paths through the environment, be it the communication network (for data or software agents) or the physical world (for embodied agents or physical resources). This thesis addresses the problem of allocating flows when the environment is mutable, either by the agents or by a malicious adversary. In this thesis I represent the environment as a graph with agents and tasks represented by source and sink nodes, respectively. The agents are partitioned
Minimum Cost Spanning Tree using Matrix Algorithm
"... Abstract A spanning tree of a connected graph is a sub graph that is a tree and connects all the verticestogether. A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight t ..."
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Abstract A spanning tree of a connected graph is a sub graph that is a tree and connects all the verticestogether. A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree. A minimum spanning tree (MST) or minimum weight spanning tree is then a spanning tree with weight less than or equal to the weight of every other spanning tree. More generally, any undirected graph (not necessarily connected) has a minimum spanning forest, which is a union of minimum spanning trees for its components. Our objective is to find minimum cost (weight) spanning tree using the algorithm which is based on the weight matrix of weighted graph.
Approximation Algorithms for the SingleSink Edge Installation Problems and Other Graph Problems
, 2004
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Approximating the Generalized Capacitated Treerouting Problem
"... In this paper, we introduce the generalized capacitated treerouting problem (GCTR), which is described as follows. Given a connected graph G = (V,E) with a sink s ∈ V and a set M ⊆ V − {s} of terminals with a nonnegative demand q(v), v ∈ M, we wish to find a collection T = {T1, T2,..., T`} of trees ..."
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In this paper, we introduce the generalized capacitated treerouting problem (GCTR), which is described as follows. Given a connected graph G = (V,E) with a sink s ∈ V and a set M ⊆ V − {s} of terminals with a nonnegative demand q(v), v ∈ M, we wish to find a collection T = {T1, T2,..., T`} of trees rooted at s to send all the demands to s, where the total demand collected by each tree Ti is bounded from above by a demand capacity κ> 0. Let λ> 0 denote a bulk capacity of an edge, and each edge e ∈ E has an installation cost w(e) ≥ 0 per bulk capacity; each edge e is allowed to have capacity kλ for any integer k, which installation incurs cost kw(e). To establish a tree routing Ti, each edge e contained in Ti requires α+βq ′ amount of capacity for the total demand q ′ that passes through edge e along Ti and prescribed constants α, β ≥ 0, where α means a fixed amount used to separate the inside of the routing Ti from the outside while term βq ′ means the net capacity proportional to q′. The objective of GCTR is to find a collection T of trees that minimizes the total installation cost of edges. Then GCTR is a new generalization of the several known multicast problems in networks with edge/demand capacities. In this paper, we prove that GCTR is (2[λ/(α + βκ)]/bλ/(α + βκ)c + ρST)approximable if λ ≥ α + βκ holds, where ρST is any approximation ratio achievable for the Steiner tree problem.