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110
Minimumenergy broadcast in allwireless networks: Npcompleteness and distribution
 In Proc. of ACM MobiCom
, 2002
"... In allwireless networks a crucial problem is to minimize energy consumption, as in most cases the nodes are batteryoperated. We focus on the problem of poweroptimal broadcast, for which it is well known that the broadcast nature of the radio transmission can be exploited to optimize energy consump ..."
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Cited by 177 (2 self)
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In allwireless networks a crucial problem is to minimize energy consumption, as in most cases the nodes are batteryoperated. We focus on the problem of poweroptimal broadcast, for which it is well known that the broadcast nature of the radio transmission can be exploited to optimize energy consumption. Several authors have conjectured that the problem of poweroptimal broadcast is NPcomplete. We provide here a formal proof, both for the general case and for the geometric one; in the former case, the network topology is represented by a generic graph with arbitrary weights, whereas in the latter a Euclidean distance is considered. We then describe a new heuristic, Embedded Wireless Multicast Advantage. We show that it compares well with other proposals and we explain how it can be distributed. Categories and Subject Descriptors
LowInterference Topology Control for Wireless Ad Hoc Networks
 ACM Wireless Networks
, 2005
"... supported by NSF CCR0311174. Abstract — Topology control has been well studied in wireless ad hoc networks. However, only a few topology control methods take into account the low interference as a goal of the methods. Some researchers tried to reduce the interference by lowering node energy consump ..."
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Cited by 79 (1 self)
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supported by NSF CCR0311174. Abstract — Topology control has been well studied in wireless ad hoc networks. However, only a few topology control methods take into account the low interference as a goal of the methods. Some researchers tried to reduce the interference by lowering node energy consumption (i.e. by reducing the transmission power) or by devising low degree topology controls, but none of those protocols can guarantee low interference. Recently, Burkhart et al. [?] proposed several methods to construct topologies whose maximum link interference is minimized while the topology is connected or is a spanner for Euclidean length. In this paper we give algorithms to construct a network topology for wireless ad hoc network such that the maximum (or average) link (or node) interference of the topology is either minimized or approximately minimized. Index Terms — Topology control, interference, wireless ad hoc networks.
Minimum energy disjoint path routing in wireless adhoc networks
 in Proceedings of the 9th Annual International Conference on Mobile Computing and Networking
, 2003
"... We develop algorithms for finding minimum energy disjoint paths in an allwireless network, for both the node and linkdisjoint cases. Our major results include a novel polynomial time algorithm that optimally solves the minimum energy 2 linkdisjoint paths problem, as well as a polynomial time algor ..."
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Cited by 70 (1 self)
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We develop algorithms for finding minimum energy disjoint paths in an allwireless network, for both the node and linkdisjoint cases. Our major results include a novel polynomial time algorithm that optimally solves the minimum energy 2 linkdisjoint paths problem, as well as a polynomial time algorithm for the minimum energy k nodedisjoint paths problem. In addition, we present efficient heuristic algorithms for both problems. Our results show that linkdisjoint paths consume substantially less energy than nodedisjoint paths. We also found that the incremental energy of additional linkdisjoint paths is decreasing. This finding is somewhat surprising due to the fact that in general networks additional paths are typically longer than the shortest path. However, in a wireless network, additional paths can be obtained at lower energy due to the broadcast nature of the wireless medium. Finally, we discuss issues regarding distributed implementation and present distributed versions of the optimal centralized algorithms presented in the paper.
Network Lifetime and Power Assignment in AdHoc Wireless Networks
 IN ESA
, 2003
"... Used for topology control in adhoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G = (V; c). The power of a vertex u in a directed spanning subgra ..."
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Cited by 53 (4 self)
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Used for topology control in adhoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G = (V; c). The power of a vertex u in a directed spanning subgraph H is given by pH(u) = maxuv2E(H) c(uv). The power of H is given by p(H) = P u2V pH(u), Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. We
Minimum energy reliable paths using unreliable wireless links
 In ACM Mobihoc
, 2005
"... We address the problem of energyefficient reliable wireless communication in the presence of unreliable or lossy wireless link layers in multihop wireless networks. Prior work [1] has provided an optimal energy efficient solution to this problem for the case where link layers implement perfect rel ..."
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Cited by 43 (0 self)
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We address the problem of energyefficient reliable wireless communication in the presence of unreliable or lossy wireless link layers in multihop wireless networks. Prior work [1] has provided an optimal energy efficient solution to this problem for the case where link layers implement perfect reliability. However, a more common scenario — a link layer that is not perfectly reliable, was left as an open problem. In this paper we first present two centralized algorithms, BAMER and GAMER, that optimally solve the minimum energy reliable communication problem in presence of unreliable links. Subsequently we present a distributed algorithm, DAMER, that approximates the performance of the centralized algorithm and leads to significant performance improvement over existing singlepath or multipath based techniques. Categories and Subject Descriptors
MinimumEnergy Broadcasting in Static Ad Hoc Wireless Networks
 Wireless Networks
, 2002
"... Energy conservation is a critical issue in ad hoc wireless networks for node and network life since the nodes are powered by batteries only. One major approach for... ..."
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Cited by 43 (5 self)
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Energy conservation is a critical issue in ad hoc wireless networks for node and network life since the nodes are powered by batteries only. One major approach for...
The power range assignment problem in radio networks on the plane
 Proc. 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS
, 2000
"... Abstract. Given a finite set S of points (i.e. the stations of a radio network) on the plane and a positive integer 1 ≤ h ≤ S  −1, the 2d Min h R. Assign. problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption provided that the transmission ..."
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Cited by 42 (7 self)
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Abstract. Given a finite set S of points (i.e. the stations of a radio network) on the plane and a positive integer 1 ≤ h ≤ S  −1, the 2d Min h R. Assign. problem consists of assigning transmission ranges to the stations so as to minimize the total power consumption provided that the transmission ranges of the stations ensure the communication between any pair of stations in at most h hops. We provide a lower bound on the total power consumption opt h (S) yielded by an optimal range assignment for any instance (S, h) of2d Min h R. Assign., for any positive constant h>0. The lower bound is a function of S, h and the minimum distance over all the pairs of stations in S. Then, we derive a constructive upper bound for the same problem as a function of S, h and the maximum distance over all the pairs of stations in S (i.e. the diameter of S). Finally, by combining the above bounds, we obtain a polynomialtime approximation algorithm for 2d Min h R. Assign. restricted to wellspread instances, for any positive constant h. Previous results for this problem were known only in special 1dimensional configurations (i.e. when points are arranged on a line).
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 42 (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.
A fast distributed approximation algorithm for minimum spanning trees
 IN PROCEEDINGS OF THE 20TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING (DISC
, 2006
"... We present a distributed algorithm that constructs an O(log n)approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ(D(G) + L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our ..."
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Cited by 35 (8 self)
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We present a distributed algorithm that constructs an O(log n)approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ(D(G) + L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our algorithm is existentially optimal (up to polylogarithmic factors), i.e., there exists graphs which need Ω(D(G) + L(G, w)) time to compute an Happroximation to the MST for any H ∈ [1, Θ(log n)]. Our result also shows that there can be a significant time gap between exact and approximate MST computation: there exists graphs in which the running time of our approximation algorithm is exponentially faster than the timeoptimal distributed algorithm that computes the MST. Finally, we show that our algorithm can be used to find an approximate MST in wireless networks and in random weighted networks in almost optimal Õ(D(G)) time.
Algorithmic, geometric and graphs issues in wireless networks
, 2002
"... We present an overview of the recent progress of applying computational geometry techniques to solve some questions, such as topology construction and broadcasting, in wireless ad hoc networks. Treating each wireless device as a node in a two dimensional plane, we model the wireless networks by unit ..."
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Cited by 33 (2 self)
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We present an overview of the recent progress of applying computational geometry techniques to solve some questions, such as topology construction and broadcasting, in wireless ad hoc networks. Treating each wireless device as a node in a two dimensional plane, we model the wireless networks by unit disk graphs in which two nodes are connected if their Euclidean distance is no more than one. We first summarize the current status of constructing sparse spanners for unit disk graphs with various combinations of the following properties: bounded stretch factor, bounded node degree, planar, and bounded total edges weight (compared with the minimum spanning tree). Instead of constructing subgraphs by removing links, we then review the algorithms for constructing a sparse backbone (connected dominating set), i.e., subgraph from the subset of nodes. We then review some efficient methods for broadcasting and multicasting with theoretic guaranteed performance.