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55
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 142 (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.
Virtual Coordinates for Ad hoc and Sensor Networks
, 2004
"... In many applications of wireless ad hoc and sensor networks, positionawareness is of great importance. Often, as in the case of geometric routing, it is sufficient to have virtual coordinates, rather than real coordinates. In this paper, we address the problem of obtaining virtual coordinates based ..."
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Cited by 56 (9 self)
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In many applications of wireless ad hoc and sensor networks, positionawareness is of great importance. Often, as in the case of geometric routing, it is sufficient to have virtual coordinates, rather than real coordinates. In this paper, we address the problem of obtaining virtual coordinates based on connectivity information. In particular, we propose the first approximation algorithm for this problem and discuss implementational aspects.
Fast Deterministic Distributed Maximal Independent Set Computation on GrowthBounded Graphs
 In Proc. of the 19th International Symposium on Distributed Computing (DISC
, 2005
"... Abstract. The distributed complexity of computing a maximal independent set in a graph is of both practical and theoretical importance. While there exists an elegant O(log n) time randomized algorithm for general graphs [20], no deterministic polylogarithmic algorithm is known. In this paper, we st ..."
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Cited by 48 (10 self)
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Abstract. The distributed complexity of computing a maximal independent set in a graph is of both practical and theoretical importance. While there exists an elegant O(log n) time randomized algorithm for general graphs [20], no deterministic polylogarithmic algorithm is known. In this paper, we study the problem in graphs with bounded growth, an important family of graphs which includes the wellknown unit disk graph and many variants thereof. Particularly, we propose a deterministic algorithm that computes a maximal independent set in time O(log ∆ · log∗n) in graphs with bounded growth, where n and ∆ denote the number of nodes and the maximal degree in G, respectively. 1
CrossLayer Latency Minimization in Wireless Networks with SINR Constraints
 MOBIHOC’07, SEPTEMBER 9–14, 2007, MONTREAL, QUEBEC, CANADA
, 2007
"... Recently, there has been substantial interest in the design of cross
layer protocols for wireless networks. These protocols optimize
certain performance metric(s) of interest (e.g. latency, energy, rate)
by jointly optimizing the performance of multiple layers of the
protocol stack. Algorithm desig ..."
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Cited by 41 (2 self)
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Recently, there has been substantial interest in the design of cross
layer protocols for wireless networks. These protocols optimize
certain performance metric(s) of interest (e.g. latency, energy, rate)
by jointly optimizing the performance of multiple layers of the
protocol stack. Algorithm designers often use geometricgraph
theoretic models for radio interference to design such crosslayer
protocols. In this paper we study the problem of designing cross
layer protocols for multihop wireless networks using a more real
istic Signal to Interference plus Noise Ratio (SINR) model for radio
interference. The following crosslayer latency minimization prob
lem is studied: Given a set V of transceivers, and a set of source
destination pairs, (i) choose power levels for all the transceivers, (ii)
choose routes for all connections, and (iii) construct an endtoend
schedule such that the SINR constraints are satisfied at each time
step so as to minimize the makespan of the schedule (the time
by which all packets have reached their respective destinations).
We present a polynomialtime algorithm with provable worstcase
performance guarantee for this crosslayer latency minimization
problem. As corollaries of the algorithmic technique we show that
a number of variants of the crosslayer latency minimization prob
lem can also be approximated efficiently in polynomial time. Our
work extends the results of Kumar et al. (Proc. SODA, 2004) and
Moscibroda et al. (Proc. MOBIHOC, 2006). Although our algo
rithm considers multiple layers of the protocol stack, it can natu
rally be viewed as compositions of tasks specific to each layer —
this allows us to improve the overall performance while preserving
the modularity of the layered structure.
Local approximation schemes for ad hoc and sensor networks
 In Proc. 3rd Joint Workshop on Foundations of Mobile Computing (DialMPOMC
, 2005
"... We present two local approaches that yield polynomialtime approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1 + ε)approximation to the problems at hand for any given ε> 0. ..."
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Cited by 39 (9 self)
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We present two local approaches that yield polynomialtime approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute 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 denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pairwise independent nodes in every rneighborhood 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.
Greedy Routing with Bounded Stretch
"... Abstract—Greedy routing is a novel routing paradigm where messages are always forwarded to the neighbor that is closest to the destination. Our main result is a polynomialtime algorithm that embeds combinatorial unit disk graphs (CUDGs – a CUDG is a UDG without any geometric information) into O(log ..."
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Cited by 29 (0 self)
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Abstract—Greedy routing is a novel routing paradigm where messages are always forwarded to the neighbor that is closest to the destination. Our main result is a polynomialtime algorithm that embeds combinatorial unit disk graphs (CUDGs – a CUDG is a UDG without any geometric information) into O(log 2 n)dimensional space, permitting greedy routing with constant stretch. To the best of our knowledge, this is the first greedy embedding with stretch guarantees for this class of networks. Our main technical contribution involves extracting, in polynomial time, a constant number of isometric and balanced tree separators from a given CUDG. We do this by extending the celebrated LiptonTarjan separator theorem for planar graphs to CUDGs. Our techniques extend to other classes of graphs; for example, for general graphs, we obtain an O(log n)stretch greedy embedding into O(log 2 n)dimensional space. The greedy embeddings constructed by our algorithm can also be viewed as a constantstretch compact routing scheme in which each node is assigned an O(log 3 n)bit label. To the best of our knowledge, this result yields the best known stretchspace tradeoff for compact routing on CUDGs. Extensive simulations on random wireless networks indicate that the average routing overhead is about 10%; only few routes have a stretch above 1.5. I.
An algorithmic approach to geographic routing in ad hoc and sensor networks
 IEEE/ACM Trans. Netw
"... Abstract—The one type of routing in ad hoc and sensor networks that currently appears to be most amenable to algorithmic analysis is geographic routing. This paper contains an introduction to the problem field of geographic routing, presents a specific routing algorithm based on a synthesis of the g ..."
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Cited by 25 (0 self)
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Abstract—The one type of routing in ad hoc and sensor networks that currently appears to be most amenable to algorithmic analysis is geographic routing. This paper contains an introduction to the problem field of geographic routing, presents a specific routing algorithm based on a synthesis of the greedy forwarding and face routing approaches, and provides an algorithmic analysis of the presented algorithm from both a worstcase and an averagecase perspective. Index Terms—Algorithmic analysis, routing, stretch, wireless networks.
Hole detection or: ”how much geometry hides in connectivity
 In Proceedings of the twentysecond annual symposium on Computational geometry
, 2006
"... Wireless sensor networks typically consist of small, very simple network nodes without any positioning device like GPS. After an initialization phase, the nodes know with whom they can talk directly, but have no idea about their relative geographic locations. We examine how much geometry information ..."
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Cited by 23 (1 self)
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Wireless sensor networks typically consist of small, very simple network nodes without any positioning device like GPS. After an initialization phase, the nodes know with whom they can talk directly, but have no idea about their relative geographic locations. We examine how much geometry information is nevertheless hidden in the communication graph of the network: Assuming that the connectivity is determined by the wellknown unitdisk graph model, we prove that using an extremely simple lineartime algorithm one can identify nodes on the boundaries of holes of the network. That is, there is enough geometry information hidden in the connectivity structure to identify topological features – in our example the holes in the network. While the theoretical analysis turns out to be quite conservative, an actual implementation shows that the algorithm works well under less stringent conditions.
Distributed localization using noisy distance and angle information
 PROCEEDINGS OF THE SEVENTH ACM INTERNATIONAL SYMPOSIUM ON MOBILE AD HOC NETWORKING AND COMPUTING
, 2006
"... Localization is an important and extensively studied problem in adhoc wireless sensor networks. Given the connectivity graph of the sensor nodes, along with additional local information (e.g. distances, angles, orientations etc.), the goal is to reconstruct the global geometry of the network. In th ..."
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Cited by 20 (5 self)
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Localization is an important and extensively studied problem in adhoc wireless sensor networks. Given the connectivity graph of the sensor nodes, along with additional local information (e.g. distances, angles, orientations etc.), the goal is to reconstruct the global geometry of the network. In this paper, we study the problem of localization with noisy distance and angle information. With no noise at all, the localization problem with both angle (with orientation) and distance information is trivial. However, in the presence of even a small amount of noise, we prove that the localization problem is NPhard. Localization with accurate distance information and relative angle information is also hard. These hardness results motivate our study of approximation schemes. We relax the nonconvex constraints to approximating convex constraints and propose linear programs (LP) for two formulations of the resulting localization problem, which we call the weak deployment and strong deployment problems. These two formulations give upper and lower bounds on the location uncertainty respectively: No sensor is located outside its weak deployment region, and each sensor can be anywhere in its strong deployment region without violating the approximate distance and angle constraints. Though LPbased algorithms are usually solved by centralized methods, we propose distributed, iterative methods, which are provably convergent to the centralized algorithm solutions. We give simulation results for the distributed algorithms, evaluating the convergence rate, dependence on measurement noises, and robustness to link dynamics.