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25
Localized construction of bounded degree and planar spanner for wireless ad hoc networks
 In DIALMPOMC
, 2003
"... We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to know its 2hop neighbors to find the edges in this new structure. Our method applies the Yao structure on the local Delauna ..."
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Cited by 69 (8 self)
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We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to know its 2hop neighbors to find the edges in this new structure. Our method applies the Yao structure on the local Delaunay graph [21] in an ordering that are computed locally. This new structure has the following attractive properties: (1) it is a planar graph; (2) its node degree is bounded from above by a positive constant 19 + ⌈ 2π α ⌉; (3) it is a tspanner (given any two nodes u and v, there is a path connecting them in the structure such that its length is no more than t ≤ max { π α,πsin 2 2 +1}·Cdel times of the shortest path in UDG); (4) it can be constructed locally and is easy to maintain when the nodes move around; (5) moreover, we show that the total communication cost is O(n), where n is the number of wireless nodes, and the computation cost of each node is at most O(d log d), where d is its 2hop neighbors in the original unit disk graph. Here Cdel is the spanning ratio of the Delaunay triangulation, which is at most 4 √ 3 9 π. And the adjustable parameter α satisfies 0 <α<π/3. In addition, experiments are conducted to show this topology is efficient in practice, compared with other wellknown topologies used in wireless ad hoc networks. Previously, only centralized method [5] of constructing bounded degree planar spanner is known, with degree bound 27 and spanning ratio t ≃ 10.02. The distributed implementation of their centralized method takes O(n 2) communications in the worst case. No localized methods were known previously for constructing bounded degree planar 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 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.
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 49 (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 algorithms for energy efficient topology in wireless ad hoc networks
 In ACM MobiHoc’04
, 2004
"... Abstract. Topology control in wireless ad hoc networks is to select a subgraph of the communication graph (when all nodes use their maximum transmission range) with some properties for energy conservation. In this paper, we propose two novel localized topology control methods for homogeneous wireles ..."
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Cited by 41 (2 self)
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Abstract. Topology control in wireless ad hoc networks is to select a subgraph of the communication graph (when all nodes use their maximum transmission range) with some properties for energy conservation. In this paper, we propose two novel localized topology control methods for homogeneous wireless ad hoc networks. Our first method constructs a structure with the following attractive properties: power efficient, bounded node degree, and planar. Its power stretch factor is at most ρ = 1 1−(2 sin π k)β, and each node only has to maintain at most k + 5 neighbors where the integer k> 6 is an adjustable parameter, and β is a real constant between 2 and 5 depending on the wireless transmission environment. It can be constructed and maintained locally and dynamically. Moreover, by assuming that the node ID and its position can be represented in O(log n) bits each for a wireless network of n nodes, we show that the structure can be constructed using at most 24n messages, where each message is O(log n) bits. Our second method improves the degree bound to k, relaxes the theoretical power spanning ratio to ρ = √ 2 β 1−(2 √ 2 sin π, where k> 8 is an adjustable parameter, and keeps all other)β k properties. We show that the second structure can be constructed using at most 3n messages, where each message has size of O(log n) bits. We also experimentally evaluate the performance of these new energy efficient network topologies. The theoretical results are corroborated by the simulations: these structures are more efficient in practice, compared with other known structures used in wireless ad hoc networks and are easier to construct. In addition, the power assignment based on our new structures shows low energy cost and small interference at each wireless node.
Fast distributed algorithm for convergecast in ad hoc geometric radio networks
 Proc. 2nd Int. Conf. on Wireless on Demand Network Systems and Service (WONS
, 2005
"... Abstract — Wireless ad hoc radio networks have gained a lot of attention in recent years. We consider geometric networks, where nodes are located in a euclidean plane. We assume that each node has a variable transmission range and can learn the distance to the closest neighbor. We also assume that n ..."
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Cited by 27 (0 self)
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Abstract — Wireless ad hoc radio networks have gained a lot of attention in recent years. We consider geometric networks, where nodes are located in a euclidean plane. We assume that each node has a variable transmission range and can learn the distance to the closest neighbor. We also assume that nodes have a special collision detection (CD) capability so that a transmitting node can detect a collision within its transmission range. We study the basic communication problem of collecting data from all nodes called convergecast. Recently, there appeared many new applications such as realtime multimedia, battlefield communications and rescue operations that impose stringent delay requirements on the convergecast time. We measure the latency of convergecast, that is the number of time steps needed to collect the data in any nnode network. We propose a very simple randomized distributed algorithm that has the expected running time O(log n). We also show that this bound is tight and any algorithm needs Ω(log n) time steps while performing convergecast in an arbitrary network. One of the most important problems in wireless ad hoc networks is to minimize the energy consumption, which maximizes the network lifetime. We study the tradeoff between the energy and the latency of convergecast. We show that our algorithm consumes at most O(n log n) times the minimum energy. We also demonstrate that for a line topology the minimum energy convergecast takes n − 1 time steps while any algorithm performing convergecast within O(log n) time steps requires Ω(n) times the minimum energy.
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.
A Unified EnergyEfficient Topology for Unicast and Broadcast
 In ACM MOBICOM
, 2005
"... We propose a novel communication efficient topology control algorithm for each wireless node to select communication neighbors and adjust its transmission power, such that all nodes together selfform a topology that is energy efficient simultaneously for both unicast and broadcast communications. W ..."
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Cited by 12 (3 self)
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We propose a novel communication efficient topology control algorithm for each wireless node to select communication neighbors and adjust its transmission power, such that all nodes together selfform a topology that is energy efficient simultaneously for both unicast and broadcast communications. We prove that the proposed topology is planar, which guarantees packet delivery if a certain localized routing method is used; it is power efficient for unicast – the energy needed to connect any pair of nodes is within a small constant factor of the minimum under a common power attenuation model; it is efficient for broadcast: the energy consumption for broadcasting data on top of it is asymptotically the best compared with structures constructed locally; it has a constant bounded logical degree, which will potentially reduce interference and signal contention. We further prove that the average physical degree of all nodes is bounded by a small constant. To the best of our knowledge, this is the first communicationefficient distributed algorithm to achieve all these properties. Previously, only a centralized algorithm was reported in [3]. Moreover, by assuming that the ID and position of every node can be represented in O(log n) bits for a wireless network of n nodes, our method uses at most 13n messages, where each message is of O(log n) bits. We also show that this structure can be efficiently updated for dynamical network environment. Our theoretical results are corroborated in the simulations.
Applications of kLocal MST for Topology Control and Broadcasting in Wireless Ad Hoc Networks
 IEEE TPDS
, 2004
"... In this paper, we propose a family of structures, namely, klocalized minimum spanning tree (LMSTk) for topology control and broadcasting in wireless ad hoc networks. We give an efficient localized method to construct LMSTk using only O(n) messages under the localbroadcast communication model, i.e. ..."
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Cited by 9 (3 self)
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In this paper, we propose a family of structures, namely, klocalized minimum spanning tree (LMSTk) for topology control and broadcasting in wireless ad hoc networks. We give an efficient localized method to construct LMSTk using only O(n) messages under the localbroadcast communication model, i.e., the signal sent by each node will be received by all nodes within the node’s transmission range. We also analytically prove that the node degree of the structure LMSTk is at most 6, LMSTk is connected and planar, and more importantly, the total edge length of the LMSTk is within a constant factor of that of the minimum spanning tree when k ≥ 2 (called low weighted hereafter). We then propose another structure, called Incident MST and RNG Graph (IMRG), that can be locally constructed using at most 13n messages under the local broadcast communication model. Test results are corroborated in the simulation study. We study the performance of our structures in terms of the total power consumption for broadcasting, the maximum node power needed to maintain the network connectivity. We theoretically prove that our structures are asymptotically the best possible for broadcasting among all locally constructed structures. Our simulations show that our new structures outperform previous locally constructed structures in terms of the broadcasting and power assignment for connectivity.
Theoretically Good Distributed CDMA/OVSF Code Assignment for Wireless Ad Hoc Networks
 Tech Report, IIT, 2004, http://www.cs.iit.edu/∼xli/publicationsselect.htm XiangYang Li and PengJun Wan
"... Abstract. We present several distributed CDMA/OVSF code assignment algorithms for wireless ad hoc networks modelled by unit disk graph (UDG). We first give a distributed code assignment whose total throughput is within a constant factor of the optimum. Then we give a distributed method such that the ..."
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Cited by 5 (0 self)
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Abstract. We present several distributed CDMA/OVSF code assignment algorithms for wireless ad hoc networks modelled by unit disk graph (UDG). We first give a distributed code assignment whose total throughput is within a constant factor of the optimum. Then we give a distributed method such that the minimum rate achieved is within a constant factor of the optimum. A distributed method that can approximate both the minimum rate and total throughput is also presented. All our methods use only O(n) total messages (each with O(log n) bits)for an ad hoc wireless network of n nodes modelled by UDG.
EnergyAware Wakeup Scheduling for Data Collection and Aggregation
"... Abstract—A sensor in wireless sensor networks (WSNs) periodically produces data as it monitors its vicinity. The basic operation in such a network is the systematic gathering (with or without innetwork aggregation) and transmitting of sensed data to a base station for further processing. A key chal ..."
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Cited by 5 (2 self)
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Abstract—A sensor in wireless sensor networks (WSNs) periodically produces data as it monitors its vicinity. The basic operation in such a network is the systematic gathering (with or without innetwork aggregation) and transmitting of sensed data to a base station for further processing. A key challenging question in WSNs is to schedule nodes ’ activities to reduce energy consumption. In this paper, we focus on designing energy efficient protocols for lowdatarate WSNs, where sensors consume different energy in different radio states (transmitting, receiving, listening, sleeping, and being idle) and also consume energy for statetransition. We design both centralized and distributed energy efficient and interferenceaware algorithms for homogeneous networks and heterogeneous networks. We use TDMA as the MAC layer protocol and schedule the sensor nodes with consecutive timeslots at different radio states while reducing the number of state transitions. We prove that the energy consumption by our scheduling for homogeneous network is at most a constant times that of the optimum and the energy consumption by our scheduling for heterogeneous network is at most Θ(log Rmax Rmin times of the optimum. We also propose efficient algorithms to construct data gathering tree such that the energy consumption and the network throughput is within a constant factor of the optimum. Extensive simulation studies show that our algorithms do reduce considerable energy consumption. Index Terms—Wireless sensor networks, energy consumption, MAC, scheduling, routing, optimization I.