Results 1  10
of
52
Approximating Steiner Networks with Node Weights
, 2007
"... The (undirected) Steiner Network problem is: given a graph G = (V, E) with edge/node weights and connectivity requirements {r(u, v) : u, v ∈ U ⊆ V}, find a minimum weight subgraph H of G containing U so that the uvedgeconnectivity in H is at least r(u, v) for all u, v ∈ U. The seminal paper of Jai ..."
Abstract

Cited by 25 (13 self)
 Add to MetaCart
(Show Context)
The (undirected) Steiner Network problem is: given a graph G = (V, E) with edge/node weights and connectivity requirements {r(u, v) : u, v ∈ U ⊆ V}, find a minimum weight subgraph H of G containing U so that the uvedgeconnectivity in H is at least r(u, v) for all u, v ∈ U. The seminal paper of Jain [19], and numerous papers preceding it, considered the EdgeWeighted Steiner Network problem, with weights on the edges only, and developed novel tools for approximating minimum weight edgecovers of several types of set functions and families. However, for the NodeWeighted Steiner Network (NWSN) problem, nontrivial approximation algorithms were known only for 0, 1 requirements. We make an attempt to change this situation, by giving the first nontrivial approximation algorithm for NWSN with arbitrary requirements. Our approximation ratio for NWSN is rmax · O(ln U), where rmax = maxu,v∈U r(u, v). This generalizes the result of Klein and Ravi [21] for the case rmax = 1. We also give an O(ln U)approximation algorithm for the nodeconnectivity variant of NWSN (when the paths are required to be internallydisjoint) for the case rmax = 2. Our results are based on a much more general approximation algorithm for the problem of finding a minimum nodeweighted edgecover of an uncrossable setfamily. We also give the first evidence that a polylogarithmic approximation ratio for NWSN might not exist even for U  = 2 and unit weights. 1 1
Minimizing interference in ad hoc and sensor networks
 In Proc. DIAL MPOMC
, 2005
"... Reducing interference is one of the main challenges in wireless communication, and particularly in ad hoc networks. The amount of interference experienced by a node v corresponds to the number of other nodes whose transmission range covers v. At the cost of communication links being dropped, interfe ..."
Abstract

Cited by 21 (3 self)
 Add to MetaCart
(Show Context)
Reducing interference is one of the main challenges in wireless communication, and particularly in ad hoc networks. The amount of interference experienced by a node v corresponds to the number of other nodes whose transmission range covers v. At the cost of communication links being dropped, interference can be reduced by decreasing the node’s transmission power. In this paper, we study the problem of minimizing the average interference while still maintaining desired network properties, such as connectivity, pointtopoint connections, or multicast trees. In particular, we present a greedy algorithm that computes an O(log n) approximation to the interference problem with connectivity requirement, where n is the number of nodes in the network. We then show the algorithm to be asymptotically optimal by proving a corresponding Ω(log n) lower bound that holds even in a more restricted interference model. Finally, we show how the algorithm can be generalized towards solving the interference problem for network properties that can be formulated as a 01 proper function.
Energyefficient wireless network design
 Theor. Comp. Sys
, 2006
"... Abstract. A crucial issue in ad hoc wireless networks is to efficiently support communication patterns that are typical in traditional (wired) networks. These include broadcasting, multicasting, and gossiping (alltoall communication). Since, in ad hoc networks energy is a scarce resource, the imp ..."
Abstract

Cited by 15 (6 self)
 Add to MetaCart
(Show Context)
Abstract. A crucial issue in ad hoc wireless networks is to efficiently support communication patterns that are typical in traditional (wired) networks. These include broadcasting, multicasting, and gossiping (alltoall communication). Since, in ad hoc networks energy is a scarce resource, the important engineering question to be solved is to guarantee a desired communication pattern minimizing the total energy consumption. Motivated by this question, we study a series of wireless network design problems and present new approximation algorithms and inapproximability results. 1
The polymatroid Steiner problems
 J. Comb. Optim
, 2005
"... Abstract. The Steiner tree problem asks for a minimum cost tree spanning a given set of terminals S ⊆ V in a weighted graph G = (V, E, c), c: E → R +. In this paper we consider a generalization of the Steiner tree problem, so called Polymatroid Steiner Problem, in which a polymatroid P = P (V) is de ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
(Show Context)
Abstract. The Steiner tree problem asks for a minimum cost tree spanning a given set of terminals S ⊆ V in a weighted graph G = (V, E, c), c: E → R +. In this paper we consider a generalization of the Steiner tree problem, so called Polymatroid Steiner Problem, in which a polymatroid P = P (V) is defined on V and the Steiner tree is required to span at least one base of P (in particular, there may be a single base S ⊆ V). This formulation is motivated by the following application in sensor networks – given a set of sensors S = {s1,..., sk}, each sensor si can choose to monitor only a single target from a subset of targets Xi, find minimum cost tree spanning a set of sensors capable of monitoring the set of all targets X = X1 ∪... ∪ Xk. The Polymatroid Steiner Problem generalizes many known Steiner tree problem formulations including the group and covering Steiner tree problems. We show that this problem can be solved with the polylogarithmic approximation ratio by a generalization of the combinatorial algorithm of Chekuri et. al. [7]. We also define the Polymatroid directed Steiner problem which asks for a minimum cost arborescence connecting a given root to a base of a polymatroid P defined on the terminal set S. We show that this problem can be approximately solved by algorithms generalizing methods of Charikar et al [6].
Minimum power configuration for wireless communication in sensor networks
 JOURNAL PUBLICATIONS AND 18 PAPERS PRESENTED IN INTERNATIONAL CONFERENCES. HIS
, 2007
"... ..."
Approximating minimum power covers of intersecting families and directed connectivity problems
 In Proc. Workshop on Approximation algorithms (APPROX), LNCS 4110
, 2006
"... Given a (directed) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we consider fundamental directed connectivity network design problems un ..."
Abstract

Cited by 13 (10 self)
 Add to MetaCart
(Show Context)
Given a (directed) graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we consider fundamental directed connectivity network design problems under the power minimization criteria. Let G = (V, E) be a graph with edgecosts {c(e) : e ∈ E} and let k be an integer. We consider finding a minimum power subgraph G of G that satisfies some prescribed property. The MinPower kOutconnected Subgraph (MPkOS) problem requires that G contains k pairwise internallydisjoint rvpaths for all v ∈ V − r, for a given ”root ” r ∈ V. The MinPower kConnected Subgraph (MPkCS) problem requires that G contains k pairwise internallydisjoint paths between every pair of its nodes. In the edge connectivity variant the paths are required to be only edge disjoint. For k = 1 all these problems are at least as hard as the SetCover problem and thus have an Ω(ln V ) approximation threshold. For k = Θ(n) the edge connectivity variants are unlikely to admit a polylogarithmic approximation algorithm [23]. We give an O(k ln V )approximation algorithms for these four problems. Our algorithms are based on a much more general O(ln V )approximation algorithm for the problem of finding a minpower directed (edge)cover of an intersecting setfamily; a setfamily F is intersecting if X ∩ Y, X ∪ Y ∈ F for any intersecting X, Y ∈ F, and an edge set F covers F if for every X ∈ F there is an edge in F entering X. 1 Introduction and
Lifetime maximization for multicasting in energyconstrained wireless networks
 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2005
"... We consider the problem of maximizing the lifetime of a given multicast connection in a wireless network of energyconstrained (e.g., batteryoperated) nodes, by choosing ideal transmission power levels for the nodes relaying the connection. We distinguish between two basic operating modes: In a st ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
(Show Context)
We consider the problem of maximizing the lifetime of a given multicast connection in a wireless network of energyconstrained (e.g., batteryoperated) nodes, by choosing ideal transmission power levels for the nodes relaying the connection. We distinguish between two basic operating modes: In a static power assignment, the power levels of the nodes are set at the beginning and remain unchanged until the nodes are depleted of energy. In a dynamic power schedule, the powers can be adjusted during operation. We show that while lifetimemaximizing static power assignments can be found in polynomial time, for dynamic schedules the problem becomes NPhard. We introduce two approximation heuristics for the dynamic case, and experimentally verify that the lifetime of a dynamically adjusted multicast connection can be made several times longer than what can be achieved by the best possible static assignment.
On Minimum Power Connectivity Problems
"... Given a (directed or undirected) graph with edge costs, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we present polynomial and improved approximation algorithms, as we ..."
Abstract

Cited by 12 (6 self)
 Add to MetaCart
Given a (directed or undirected) graph with edge costs, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we present polynomial and improved approximation algorithms, as well as inapproximability results, for some classic network design problems under the power minimization criteria. In particular, for the problem of finding a minpower subgraph that contains k internallydisjoint vspaths from every node v to a given node s, we give a polynomial algorithm for directed graphs and a logarithmic approximation algorithm for undirected graphs. In contrast, we will show that the corresponding edgeconnectivity problems are unlikely to admit a polylogarithmic approximation.
Survivable Network Design Problems in Wireless Networks
"... Survivable network design is an important suite of algorithmic problems where the goal is to select a minimum cost network subject to the constraint that some desired connectivity property has to be satisfied by the network. Traditionally, these problems have been studied in a model where individual ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
(Show Context)
Survivable network design is an important suite of algorithmic problems where the goal is to select a minimum cost network subject to the constraint that some desired connectivity property has to be satisfied by the network. Traditionally, these problems have been studied in a model where individual edges (and sometimes nodes) have an associated cost. This model does not faithfully represent wireless networks, where the activation of an edge is dependent on the selection of parameter values at its endpoints, and the cost incurred is a function of these values. We present a realistic optimization model for the design of survivable wireless networks that generalizes various connectivity problems studied in the theory literature, e.g. nodeweighted steiner network, power optimization, minimum connected dominating set, and in the networking literature, e.g. installation cost optimization, minimum broadcast tree. We obtain the following algorithmic results for our general model: 1. For k = 1 and 2, we give O(log n)approximation algorithms for both the vertex and edge connectivity versions of the kconnectivity problem. These results are tight (up to constants); we show that even for k = 1, it is NPhard to obtain an approximation factor of o(log n). 2. For the minimum steiner network problem, we give a tight (up to constants) O(log n)approximation algorithm. 3. We give a reduction from the kedge connectivity problem to a more tractable degreeconstrained problem. This involves proving new connectivity theorems that might be of independent interest. We apply this result to obtain new approximation algorithms in the power optimization and installation cost optimization applications. 1
An Exponential Improvement on the MST Heuristic for Minimum Energy Broadcasting in Ad Hoc Wireless Networks
"... In this paper we present a new approximation algorithm for the Minimum Energy Broadcast Routing (MEBR) problem in ad hoc wireless networks that has exponentially better approximation factor than the wellknown Minimum Spanning Tree (MST) heuristic. Namely, for any instance where a minimum spanning ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
(Show Context)
In this paper we present a new approximation algorithm for the Minimum Energy Broadcast Routing (MEBR) problem in ad hoc wireless networks that has exponentially better approximation factor than the wellknown Minimum Spanning Tree (MST) heuristic. Namely, for any instance where a minimum spanning tree of the set of stations is guaranteed to cost at most ρ times the cost of an optimal solution for MEBR, we prove that our algorithm achieves an approximation ratio bounded by 2 ln ρ − 2 ln 2 + 2. This result is particularly relevant for its consequences on Euclidean instances where we significantly improve previous results.