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72
AdHoc Networks Beyond Unit Disk Graphs
, 2003
"... In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer ..."
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Cited by 116 (11 self)
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In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that  in comparison to the cost known on Unit Disk Graphs  the complexity results in this model contain the additional factor 1/d&sup2;. We prove that in Quasi Unit Disk Graphs flooding is an asymptotically messageoptimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.
Does Topology Control Reduce Interference
 In Proceedings of the 5 th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC
, 2004
"... Topology control in adhoc networks tries to lower node energy consumption by reducing transmission power and by confining interference, collisions and consequently retransmissions. Commonly low interference is claimed to be a consequence to sparseness of the resulting topology. In this paper we dis ..."
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Cited by 100 (8 self)
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Topology control in adhoc networks tries to lower node energy consumption by reducing transmission power and by confining interference, collisions and consequently retransmissions. Commonly low interference is claimed to be a consequence to sparseness of the resulting topology. In this paper we disprove this implication. In contrast to most of the related work—claiming to solve the interference issue by graph sparseness without providing clear argumentation or proofs—, we provide a concise and intuitive definition of interference. Based on this definition we show that most currently proposed topology control algorithms do not effectively constrain interference. Furthermore we propose connectivitypreserving and spanner constructions that are interferenceminimal.
XTC: A Practical Topology Control Algorithm for AdHoc Networks
 In 4th International Workshop on Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks (WMAN
, 2003
"... The XTC adhoc network topology control algorithm introduced in this paper shows three main advantages over previously proposed algorithms. First, it is extremely simple and strictly local. Second, it does not assume the network graph to be a Unit Disk Graph; XTC proves correct also on general weigh ..."
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Cited by 69 (9 self)
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The XTC adhoc network topology control algorithm introduced in this paper shows three main advantages over previously proposed algorithms. First, it is extremely simple and strictly local. Second, it does not assume the network graph to be a Unit Disk Graph; XTC proves correct also on general weighted network graphs. Third, the algorithm does not require availability of node position information. Instead, XTC operates with a general notion of order over the neighbors' link qualities. In the special case of the network graph being a Unit Disk Graph, the resulting topology proves to have bounded degree, to be a planar graph, andon averagecase graphsto be a good spanner.
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 66 (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.
Localized Delaunay Triangulation with Application in Ad Hoc Wireless Networks
 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS
, 2003
"... Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RNG) or Gabriel graph (GG) is used as such planar structure. However, it is wellknown that the spanning ratios of these two grap ..."
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Cited by 59 (8 self)
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Several localized routing protocols guarantee the delivery of the packets when the underlying network topology is a planar graph. Typically, relative neighborhood graph (RNG) or Gabriel graph (GG) is used as such planar structure. However, it is wellknown that the spanning ratios of these two graphs are not bounded by any constant (even for uniform randomly distributed points). Bose et al. [11] recently developed a localized routing protocol that guarantees that the distance traveled by the packets is within a constant factor of the minimum if Delaunay triangulation of all wireless nodes is used, in addition, to guarantee the delivery of the packets. However, it is expensive to construct the Delaunay triangulation in a distributed manner. Given a set of wireless nodes, we model the network as a unitdisk graph (UDG), in which a link uv exists only if the distance kuvk is at most the maximum transmission range. In this paper, we present a novel localized networking protocol that constructs a planar 2.5spanner of UDG, called the localized Delaunay triangulation (LDEL), as network topology. It contains all edges that are both in the unitdisk graph and the Delaunay triangulation of all nodes. The total communication cost of our networking protocol is Oðn log nÞ bits, which is within a constant factor of the optimum to construct any structure in a distributed manner. Our experiments show that the delivery rates of some of the existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies. Our simulations also show that the traveled distance of the packets is significantly less when the FACE routing algorithm is applied on LDEL, rather than applied on GG.
Localized Topology Control for Heterogeneous Wireless Adhoc Networks
"... We study topology control in heterogeneous wireless ad hoc networks, where mobile hosts may have different maximum transmission powers and two nodes are connected iff they are within the maximum transmission range of each other. We present several strategies that all wireless nodes selfmaintain sp ..."
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Cited by 54 (11 self)
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We study topology control in heterogeneous wireless ad hoc networks, where mobile hosts may have different maximum transmission powers and two nodes are connected iff they are within the maximum transmission range of each other. We present several strategies that all wireless nodes selfmaintain sparse and power efficient topologies in heterogeneous network environment with low communication cost. The first structure is sparse and can be used for broadcasting. While the second structure keeps the minimum power consumption path, and the third structure is a length and power spanner with a bounded degree. Both the second and third structures are power efficient and can be used for unicast. Here a structure is power efficient if the total power consumption of the least cost path connecting any two nodes in it is no more than a small constant factor of that in the original heterogeneous communication graph. All our methods use at most O(n) total messages, where each message has O(log n) bits.
A ConeBased Distributed TopologyControl Algorithm for Wireless MultiHop Networks
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2002
"... The topology of a wireless multihop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a conebased distributed topology control algorithm. This algorithm does not assume that nodes have GPS information available; rather it dep ..."
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Cited by 43 (1 self)
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The topology of a wireless multihop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a conebased distributed topology control algorithm. This algorithm does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node u transmits with the minimum power p u,# required to ensure that in every cone of degree # around u, there is some node that u can reach with power p u,# . We show that taking # = 5#/6 is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from s to t when every node communicates at maximum power then, if # 5#/6, there is still a path in the smallest symmetric graph G # containing all edges (u, v) such that u can communicate with v using power p u,# . On the other hand, if # > 5#/6,
A Robust Interference Model for Wireless Ad Hoc Networks
 5th International Workshop on Algorithms for Wireless, Mobile, Ad Hoc and Sensor Networks (WMAN
, 2005
"... Among the foremost goals of topology control in wireless adhoc networks is interference reduction. This paper presents a receivercentric interference model featuring two main advantages over previous work. First, it reflects the fact that interference occurs at the intended receiver of a message. ..."
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Cited by 38 (5 self)
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Among the foremost goals of topology control in wireless adhoc networks is interference reduction. This paper presents a receivercentric interference model featuring two main advantages over previous work. First, it reflects the fact that interference occurs at the intended receiver of a message. Second, the presented interference measure is robust with respect to addition or removal of single network nodes. Regarding both of these aspects our model intuitively corresponds to the behavior of interference in reality. Based on this interference model, we show that currently known topology control algorithms poorly reduce interference. Motivated by the observation that already onedimensional network instances display the intricacy of the considered problem, we continue to focus on the socalled highway model. Setting out to analyze the special case of the exponential node chain, we eventually describe an algorithm guaranteeing to achieve a 4 √ ∆approximation of the optimal connectivitypreserving topology in the general highway model. 1.
Efficient Construction of Low Weight Bounded Degree Planar Spanner
 International Journal of Computational Geometry and Applications
, 2003
"... Given a set V of n points in a twodimensional plane, we give an O(n log n)time centralized algorithm that constructs a planar tspanner for V, for t <= +1} C del , such that the degree of each node is bounded from above by 19 + and the total edge length is proportional to the weight of the mini ..."
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Cited by 18 (5 self)
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Given a set V of n points in a twodimensional plane, we give an O(n log n)time centralized algorithm that constructs a planar tspanner for V, for t <= +1} C del , such that the degree of each node is bounded from above by 19 + and the total edge length is proportional to the weight of the minimum spanning tree of V , where 0 < # < #/2 is an adjustable parameter...
Interference Arises at the Receiver
 In Proceedings of Int. Conference on Wireless Networks, Communications, and Mobile Computing (WIRELESSCOM
, 2005
"... Abstract — Energy consumption in general and interference in particular being among the most critical issues in wireless networks, this paper introduces an explicit definition of interference, based on the number of other nodes by which a given network node can be disturbed. With this definition we ..."
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Cited by 12 (4 self)
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Abstract — Energy consumption in general and interference in particular being among the most critical issues in wireless networks, this paper introduces an explicit definition of interference, based on the number of other nodes by which a given network node can be disturbed. With this definition we show that there exist instances of sensor networks in which no topology control algorithm—aiming at interference reduction by having nodes restrict their transmission power levels—can construct a valid data gathering network with interference less than logarithmic in the number of network nodes n. In a second part of the paper we introduce the Nearest Component Connector (NCC) algorithm, which asymptotically matches this lower bound, guaranteeing to build a valid topology with interference in O(log n) in any given sensor network. Finally the paper compares NCC to other previously proposed data gathering structures in averagecase networks. I.