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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 129 (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 56 (0 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.
Network Lifetime and Power Assignment in AdHoc Wireless Networks
 in ESA
, 2003
"... Abstract. 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 spanni ..."
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Cited by 42 (3 self)
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Abstract. 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
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 37 (9 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).
Some Recent Theoretical Advances and Open Questions on Energy Consumption in AdHoc Wireless Networks
, 2002
"... One of the main benefits of power controlled adhoc wireless networks is their ability to vary the range in order to reduce the power consumption. Minimizing energy consumption is crucial on such kind of networks since, typically, wireless devices are portable and benefit only of limited power resou ..."
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Cited by 30 (9 self)
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One of the main benefits of power controlled adhoc wireless networks is their ability to vary the range in order to reduce the power consumption. Minimizing energy consumption is crucial on such kind of networks since, typically, wireless devices are portable and benefit only of limited power resources. On the other hand, the network must have a sufficient degree of connectivity in order to guarantee fast and efficient communication. These two aspects yield a class of fundamental optimization problems, denoted as range assignment problems, that have been the subject of several works in the area of wireless network theory. The primary aim of this paper is to describe the most important recent advances on this class of problems. Rather than completeness, the paper will try to provide results and techniques that seem to be the most promising to address the several important related problems which are still open. Discussing such related open problems are indeed our other main goal.
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 30 (3 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...
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.
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 24 (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
Algorithmic, Geometric and Graphs Issues in Wireless Networks
 Wireless Communications and Mobile Computing
, 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 24 (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 rst 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 ecient methods for broadcasting and multicasting with theoretic guaranteed performance.
Power efficient range assignment for symmetric connectivity in static adhoc wireless networks. Wireless Networks
 Wireless Networks
, 2006
"... In this paper we study the problem of assigning transmission ranges to the nodes of a static ad hoc wireless network so as to minimize the total power consumed under the constraint that enough power is provided to the nodes to ensure that the network is connected. We focus on the MINPOWER SYMMETRIC ..."
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Cited by 19 (1 self)
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In this paper we study the problem of assigning transmission ranges to the nodes of a static ad hoc wireless network so as to minimize the total power consumed under the constraint that enough power is provided to the nodes to ensure that the network is connected. We focus on the MINPOWER SYMMETRIC CONNECTIVITY problem, in which the bidirectional links established by the transmission ranges are required to form a connected graph. Implicit in previous work on transmission range assignment under asymmetric connectivity requirements is the proof that MINPOWER SYMMETRIC CONNECTIVITY is NPhard and that the MST algorithm has an approximation ratio of 2. In this paper we make the following contributions: (1) we show that the related MINPOWER SYMMETRIC UNICAST problem can be solved efficiently by a shortestpath computation in an appropriately constructed graph. (2) we give an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up to 3540 nodes in 1 hour; (3) we establish the similarity between MINPOWER SYMMETRIC CONNECTIVITY and the classic STEINER TREE problem in graphs, and use this similarity to give a polynomialtime approximation scheme with performance ratio approaching 5/3 as well as a more practical approximation algorithm with approximation factor 11/6; and (4) we give a comprehensive experimental study comparing new and previously proposed heuristics with the above exact and approximation algorithms.