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107
On The Symmetric Range Assignment Problem In Wireless Ad Hoc Networks
, 2002
"... In this paper we consider a constrained version of the range assignment problem for wireless ad hoc networks, where the value the node transmitting ranges must be assigned in such a way that the resulting communication graph is strongly connected and the energy cost is minimum. We impose the further ..."
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Cited by 38 (1 self)
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In this paper we consider a constrained version of the range assignment problem for wireless ad hoc networks, where the value the node transmitting ranges must be assigned in such a way that the resulting communication graph is strongly connected and the energy cost is minimum. We impose the further requirement of symmetry on the resulting communication graph. We also consider a weaker notion of symmetry, in which only the existence of a set of symmetric edges that renders the communication graph connected is required. Our interest in these problems is motivated by the fact that a (weakly) symmetric range assignment can be more easily integrated with existing higher and lowerlevel protocols for ad hoc networks, which assume that all the nodes have the same transmitting range. We show that imposing symmetry does not change the complexity of the problem, which remains NPhard in two and threedimensional networks. We also show that a weakly symmetric range assignment can reduce the energy cost considerably with respect to the homogeneous case, in which all the nodes have the same transmitting range, and that no further (asymptotic) bene t is expected from the asymmetric range assignment. Hence, the results presented in this paper indicate that weak symmetry is a desirable property of the range assignment.
A ReservationBased Multicast (RBM) Routing Protocol for Mobile Networks: Initial Route Construction Phase
, 1995
"... We propose a combined multicast routing and resource reservation protocol, termed ReservationBased Multicast (RBM), that performs routing in a fashion similar to Protocol Independent Multicast (PIM), but which is intended for mobile operation and routes hierarchicallyencoded data streams based on ..."
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Cited by 34 (0 self)
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We propose a combined multicast routing and resource reservation protocol, termed ReservationBased Multicast (RBM), that performs routing in a fashion similar to Protocol Independent Multicast (PIM), but which is intended for mobile operation and routes hierarchicallyencoded data streams based on userspecified fidelity requirements, realtime delivery thresholds and prevailing network bandwidth constraints. The protocol retains the fully distributed operation, scalability and receiverinitiated orientation of PIM; but, unlike PIM, the protocol is tightly coupled to an underlying, distributed, unicast routing protocol thereby facilitating operation in a dynamic topology. This paper focuses on the initial route construction phase, assumed to occur during a static "snapshot" of the dynamic topology, and is therefore applicable to fixed networks as well, e.g. the Internet. A forthcoming paper will detail the protocol's robustness and adaptivity to arbitrary topological changes during bot...
Computing NearOptimal Solutions to Combinatorial Optimization Problems
 IN COMBINATORIAL OPTIMIZATION, DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1995
"... In the past few years, there has been significant progress in our understanding of the extent to which nearoptimal solutions can be efficiently computed for NPhard combinatorial optimization problems. This paper surveys these recent developments, while concentrating on the advances made in the ..."
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Cited by 31 (0 self)
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In the past few years, there has been significant progress in our understanding of the extent to which nearoptimal solutions can be efficiently computed for NPhard combinatorial optimization problems. This paper surveys these recent developments, while concentrating on the advances made in the design and analysis of approximation algorithms, and in particular, on those results that rely on linear programming and its generalizations.
An Improved LPbased Approximation for Steiner Tree
, 2009
"... The Steiner tree problem is one of the most fundamentalhard problems: given a weighted undirected graph and a subset of terminal nodes, find a minimum weight tree spanning the terminals. In a sequence of papers, the approximation ratio for this problem was improved from to the current best���[Robin ..."
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Cited by 28 (0 self)
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The Steiner tree problem is one of the most fundamentalhard problems: given a weighted undirected graph and a subset of terminal nodes, find a minimum weight tree spanning the terminals. In a sequence of papers, the approximation ratio for this problem was improved from to the current best���[Robins,ZelikovskySIDMA’05]. All these algorithms are purely combinatorial. A longstanding open problem is whether there is an LPrelaxation for Steiner tree with integrality gap smaller than [Vazirani,RajagopalanSODA’99]. In this paper we improve the approximation factor for Steiner tree, developing an LPbased approximation a� algorithm. Our algorithm is based on a, seemingly novel, iterative randomized rounding technique. We consider a directedcomponent cut relaxation for the�restricted Steiner tree problem. We sample one of these components with probability proportional to the value of the associated variable in the optimal fractional solution and contract it. We iterate this process for a proper number of times and finally output the sampled components together
A Comparison of Multicast Trees and Algorithms
, 1994
"... . Multicast trees can be shared across sources or may be sourcespecific. Inspired by recent interests in using shared trees for interdomain multicasting [BFC93] [WLE + 92], this paper investigates the tradeoffs among different algorithms and tree types. Because of the dynamic nature of grap ..."
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Cited by 26 (3 self)
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. Multicast trees can be shared across sources or may be sourcespecific. Inspired by recent interests in using shared trees for interdomain multicasting [BFC93] [WLE + 92], this paper investigates the tradeoffs among different algorithms and tree types. Because of the dynamic nature of graphs, only worst case delay bounds can be calculated using analytical methods. We present simulation results over random graphs that demonstrate the performance of these trees, under different circumstances. We evaluate the performance in terms of path length, link cost, and traffic concentrations. Draft submitted to INFOCOM'94 1 Introduction Pointtomultipoint communications will play a critical role in future computer networks. The problem of computing the optimal multicast path, in the shape of a tree or a group of trees, has many potential solutions; however, to date there have not been systematic comparisons among the different solutions. Today's multicast applications are prima...
An Optimal Bound for the MST Algorithm to Compute Energy Efficient Broadcast Trees in Wireless Networks
 IN ICALP
, 2005
"... Computing energy efficient broadcast trees is one of the most prominent operations in wireless networks. For stations embedded in the Euclidean plane, the best analytic result known to date is a 6.33approximation algorithm based on computing an Euclidean minimum spanning tree. We improve the analy ..."
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Cited by 25 (0 self)
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Computing energy efficient broadcast trees is one of the most prominent operations in wireless networks. For stations embedded in the Euclidean plane, the best analytic result known to date is a 6.33approximation algorithm based on computing an Euclidean minimum spanning tree. We improve the analysis of this algorithm and show that its approximation ratio is 6, which matches a previously known lower bound for this algorithm.
An efficient algorithm for minimizing a sum of Euclidean norms with applications
 SIAM Journal on Optimization
, 1997
"... Abstract. In recent years rich theories on polynomialtime interiorpoint algorithms have been developed. These theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications. In this paper, the problem of minimizing a sum o ..."
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Cited by 22 (4 self)
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Abstract. In recent years rich theories on polynomialtime interiorpoint algorithms have been developed. These theories and algorithms can be applied to many nonlinear optimization problems to yield better complexity results for various applications. In this paper, the problem of minimizing a sum of Euclidean norms is studied. This problem is convex but not everywhere differentiable. By transforming the problem into a standard convex programming problem in conic form, we show that an ɛoptimal solution can be computed efficiently using interiorpoint algorithms. As applications to this problem, polynomialtime algorithms are derived for the Euclidean single facility location problem, the Euclidean multifacility location problem, and the shortest network under a given tree topology. In particular, by solving the Newton equation in linear time using Gaussian elimination on leaves of a tree, we present an algorithm which computes an ɛoptimal solution to the shortest network under a given full Steiner topology interconnecting N regular points, in O(N √ N(log(¯c/ɛ)+ log N)) arithmetic operations where ¯c is the largest pairwise distance among the given points. The previous bestknown result on this problem is a graphical algorithm which requires O(N 2) arithmetic operations under certain conditions. Key words. polynomial time, interiorpoint algorithm, minimizing a sum of Euclidean norms, Euclidean facilities location, shortest networks, Steiner minimum trees
Improved Approximation Schemes for Geometrical Graphs Via Spanners and Banyans
 In 30th ACM Symposium on Theory of Computing (STOC'98
, 1998
"... We give deterministic and randomized algorithms to find a Euclidean traveling salesman tour (TST) of length within (1 + 1=s) times optimal. They run in O(N log N) time and O(N) space for constant dimension and s. These time and space bounds are optimal in an algebraic computation tree model. We can ..."
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Cited by 17 (2 self)
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We give deterministic and randomized algorithms to find a Euclidean traveling salesman tour (TST) of length within (1 + 1=s) times optimal. They run in O(N log N) time and O(N) space for constant dimension and s. These time and space bounds are optimal in an algebraic computation tree model. We can also find a (1 + 1=s) times optimal length 2matching (M2M), edge cover (EC), minimum spanning tree (MST), Steiner minimal tree (SMT), rectilinear ditto (RSMT), and related graphs in the same time bound. This improves recent algorithms of Arora, which had used N(log N) O(s d\Gamma1 ) time in fixed dimension d to produce a (1 + 1=s) times optimal TST (or SMT, RSMT) with success probability 1=2. To verify success, however, Arora could only use a deterministic version of his algorithm that took a factor of N d more time. The increase in running time for our deterministic version depends only on s. Arora's approach can also be extended to produce other (1 + ffl)approximate geometrical grap...
An Approximation Algorithm for the Multicast Congestion Problem via Minimum Steiner Trees
 In 3rd International Workshop on Approximation and Randomized Algorithms in Communication Networks (ARANCE
, 2002
"... We are given a graph G = (V;E) to represent a communication network where jV j = n and jEj = m and a set of multicast requests S 1 , : : : , S k V . ..."
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Cited by 17 (3 self)
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We are given a graph G = (V;E) to represent a communication network where jV j = n and jEj = m and a set of multicast requests S 1 , : : : , S k V .