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Constant-factor approximation for minimum-weight (connected) dominating sets in unit disk graphs
- In: Proc. of the 9 th Int. Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX). (2006
, 2006
"... For a given graph with weighted vertices, the goal of the minimum-weight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph is contained in the subset or has a neighbor in the subset. A unit disk graph is a graph in which each vertex correspond ..."
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Cited by 42 (5 self)
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For a given graph with weighted vertices, the goal of the minimum-weight dominating set problem is to compute a vertex subset of smallest weight such that each vertex of the graph is contained in the subset or has a neighbor in the subset. A unit disk graph is a graph in which each vertex corresponds to a unit disk in the plane and two vertices are adjacent if and only if their disks have a non-empty intersection. We present the first constant-factor approximation algorithm for the minimum-weight dominating set problem in unit disk graphs, a problem motivated by applications in wireless ad-hoc networks. The algorithm is obtained in two steps: First, the problem is reduced to the problem of covering a set of points located in a small square using a minimumweight set of unit disks. Then, a constant-factor approximation algorithm for the latter problem is obtained using enumeration and dynamic programming techniques exploiting the geometry of unit disks. Furthermore, we show how to obtain a constant-factor approximation algorithm for the minimum-weight connected dominating set problem in unit disk graphs. Our techniques also yield a constant-factor approximation algorithm for the weighted disk cover problem (covering a set of points in the plane with unit disks of minimum total weight) and a 3-approximation algorithm for the weighted forwarding set problem (covering a set of points in the plane with weighted unit disks whose centers are all contained in a given unit disk). 1
Local approximation schemes for ad hoc and sensor networks
- In Proc. 3rd Joint Workshop on Foundations of Mobile Computing (DialM-POMC
, 2005
"... We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Indepen-dent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and com-pute a (1 + ε)-approximation to the problems at hand for any given ε> 0. ..."
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Cited by 40 (9 self)
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We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Indepen-dent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and com-pute a (1 + ε)-approximation to the problems at hand for any given ε> 0. The time complexity of both algorithms is O(TMIS + log ∗n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n de-notes the number of nodes. We then extend these results to a more general class of graphs in which the maximum num-ber of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs.
Analyzing the Energy-Latency Trade-off during the Deployment of Sensor Networks
- In Proc. IEEE Infocom
, 2006
"... Abstract — The inherent trade-off between energy-efficiency and rapidity of event dissemination is characteristic for wireless sensor networks. Scarcity of energy renders it necessary for nodes to spend a large portion of their lifetime in an energyefficient sleep mode during which they do neither r ..."
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Cited by 24 (5 self)
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Abstract — The inherent trade-off between energy-efficiency and rapidity of event dissemination is characteristic for wireless sensor networks. Scarcity of energy renders it necessary for nodes to spend a large portion of their lifetime in an energyefficient sleep mode during which they do neither receive nor send messages. On the other hand, the longer nodes stay in sleep mode, the slower will be the reaction time for disseminating an external event. The trade-off is prominently exhibited during the deployment phase of sensor networks, if some nodes are deployed earlier than others. In this paper, we study this fundamental trade-off by giving a formal model that enables us to compare the performance of different protocols and algorithms. Based on this model, we propose, analyze, and simulate two novel algorithms which significantly outperform existing solutions. I.
Clustering wireless ad hoc networks with weakly connected dominating set
, 2007
"... The increasing popular personal communications and mobile computing require a wireless network infrastructure that supports selfconfiguration and self-management. Efficient clustering protocol for constructing virtual backbone is becoming one of the most important issues in wireless ad hoc networks. ..."
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Cited by 16 (0 self)
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The increasing popular personal communications and mobile computing require a wireless network infrastructure that supports selfconfiguration and self-management. Efficient clustering protocol for constructing virtual backbone is becoming one of the most important issues in wireless ad hoc networks. The weakly connected dominating set (WCDS) is very suitable for cluster formation. As finding the minimum WCDS in an arbitrary graph is a NP-Hard problem, we propose an area-based distributed algorithm for WCDS construction in wireless ad hoc networks with time and message complexity O(n). This Area algorithm is divided into three phases: area partition, WCDS construction for each area and adjustment along the area borders. We confirm the effectiveness of our algorithm through analysis and comprehensive simulation study. The number of nodes in the WCDS constructed by this Area algorithm is up to around 50 % less than that constructed by the previous well-known algorithm.
ART: an asymmetric and reliable transport mechanism for wireless sensor networks
- International Journal of Sensor Networks
, 2007
"... Many applications developed for wireless sensor networks (WSNs) demand for Re-liable communication service, since majority of these applications are event-critical applications. There has been a vast body of knowledge on reliable data transfer in wireless networks; however, many of those solutions a ..."
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Cited by 16 (0 self)
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Many applications developed for wireless sensor networks (WSNs) demand for Re-liable communication service, since majority of these applications are event-critical applications. There has been a vast body of knowledge on reliable data transfer in wireless networks; however, many of those solutions are not applicable to WSNs due to the fact that they address the problem by oering per message transport reliabil-ity. However, densely deployed sensor nodes can generate many redundant messages that essentially indicate the same event from the area of interest, this message-level reliability usually poses signicantly high and unnecessary communication costs. In this paper, we address the problem of reliable data transferring by rst dening event reliability and query reliability to match the unique characteristics of WSNs. Unlike other studies on transport protocols for WSN, we consider event delivery in conjunction with query delivery. For the purpose, we propose an energy-aware sensor classi cation algorithm to construct a network topology that is composed of sensors in providing desired level of event and query reliability. Using such an approach, reliability is granted in the sense that critical event reports are received by the sink
T.: Distributed approximation of capacitated dominating sets
- In: Proc. 19th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA
, 2007
"... We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) ∈ N for each node v ∈ V, the CapMDS problem asks for a subset S ⊆ V of minimal cardin ..."
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Cited by 15 (1 self)
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We study local, distributed algorithms for the capacitated minimum dominating set (CapMDS) problem, which arises in various distributed network applications. Given a network graph G = (V, E), and a capacity cap(v) ∈ N for each node v ∈ V, the CapMDS problem asks for a subset S ⊆ V of minimal cardinality, such that every network node not in S is covered by at least one neighbor in S, and every node v ∈ S covers at most cap(v) of its neighbors. We prove that in general graphs and even with uniform capacities, the problem is inherently non-local, i.e., every distributed algorithm achieving a non-trivial approximation ratio must have a time complexity that essentially grows linearly with the network diameter. On the other hand, if for some parameter ɛ> 0, capacities can be violated by a factor of 1 + ɛ, CapMDS becomes much more local. Particularly, based on a novel distributed randomized rounding technique, we present a distributed bi-criteria algorithm that achieves an O(log ∆)-approximation in time O(log 3 n + log(n)/ɛ), where n and ∆ denote the number of nodes and the maximal degree in G, respectively. Finally, we prove that in geometric network graphs typically arising in wireless settings, the uniform problem can be approximated within a constant factor in logarithmic time, whereas the non-uniform problem remains entirely non-local.
Weighted Steiner connected dominating set and its application to multicast routing
- in wireless MANETs, Wireless Personal Communications
"... In this paper, we first propose three centralized learning automata-based heuristic algorithms for approximating a near optimal solution to the minimum weight Steiner connected dominating set (WSCDS) problem. Finding the Steiner connected dominating set of the network graph is a promising approach f ..."
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Cited by 14 (6 self)
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In this paper, we first propose three centralized learning automata-based heuristic algorithms for approximating a near optimal solution to the minimum weight Steiner connected dominating set (WSCDS) problem. Finding the Steiner connected dominating set of the network graph is a promising approach for multicast routing in wireless ad-hoc networks. Therefore, we present a distributed implementation of the last approximation algorithm proposed in this paper (Algorithm III) for multicast routing in wireless mobile ad-hoc networks. The proposed WSCDS algorithms are compared with the well-known existing algorithms and the obtained results show that Algorithm III outperforms the others both in terms of the dominating set size and running time. Our simulation experiments also show the superiority of the proposed multicast routing algorithm over the best previous methods in terms of the packet delivery ratio, multicast route lifetime, and end-to-end delay.
Simple Approximation Algorithms and PTASs for Various Problems in Wireless Ad Hoc Networks
, 2005
"... A wireless ad hoc network is often composed of a set V of n wireless devices distributed in a two-dimensional domain. For each wireless device (also called node) u ∈ V, there is a transmission region within which signal-to-noise-ratio (SNR) is at least a threshold γ so that the signal transmitted by ..."
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Cited by 9 (6 self)
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A wireless ad hoc network is often composed of a set V of n wireless devices distributed in a two-dimensional domain. For each wireless device (also called node) u ∈ V, there is a transmission region within which signal-to-noise-ratio (SNR) is at least a threshold γ so that the signal transmitted by u can be correctly received by other nodes with high probability. The transmission region is often modeled as a disk centered at the node u. In addition, for each node u, there is an interference region within which the transmission from u makes the signal-to-interference-andnoise-ratio (SINR) of the legitimate receiver smaller than the threshold γ so that the legitimate receiver cannot correctly receive the message from the legitimate transmitter. In this paper, we first present new graph models to model the communication graphs and the interference graphs defined by wireless ad hoc networks with attention to interference-free channel assignment or scheduling. Then we propose some simple approximation algorithms and/or PTASs (polynomial time approximation scheme) to approximate several classical graph problems such as maximum independent set, minimum vertex cover and minimum vertex coloring in these graph models. In addition, we also discuss various possible applications for these simple approximation algorithms and/or PTASs in wireless ad hoc networks.
Backbone construction in selfish wireless networks
- PROC. ACM INTERNATIONAL CONFERENCE ON MEASUREMENT AND MODELING OF COMPUTER SYSTEMS
, 2007
"... We present a protocol to construct routing backbones in wireless networks composed of selfish participants. Backbones are inherently cooperative, so constructing them in selfish environments is particularly difficult; participants want a backbone to exist (so others relay their packets) but do not w ..."
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Cited by 8 (2 self)
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We present a protocol to construct routing backbones in wireless networks composed of selfish participants. Backbones are inherently cooperative, so constructing them in selfish environments is particularly difficult; participants want a backbone to exist (so others relay their packets) but do not want to join the backbone (so they do not have to relay packets for others). We model the wireless backbone as a public good and use impatience as an incentive for cooperation. To determine if and when to donate to this public good, each participant calculates how patient it should be in obtaining the public good. We quantify patience using the Volunteer’s Timing Dilemma (VTD), which we extend to general multihop network settings. Using our generalized VTD analysis, each node individually computes as its dominant strategy the amount of time to wait before joining the backbone. We evaluate our protocol using both simulations and an implementation. Our results show that, even though participants in our system deliberately wait before volunteering, a backbone is formed quickly. Further, the quality of the backbone (such as the size and resulting network lifetime) is comparable to that of existing backbone protocols that assume altruistic behavior.
