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12
PolynomialTime Approximation Schemes for Geometric Graphs
, 2001
"... A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weigh ..."
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Cited by 104 (5 self)
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A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weight) and for the minimum weight vertex cover problem in disk graphs. These are the first known PTASs for NPhard optimization problems on disk graphs. They are based on a novel recursive subdivision of the plane that allows applying a shifting strategy on different levels simultaneously, so that a dynamic programming approach becomes feasible. The PTASs for disk graphs represent a common generalization of previous results for planar graphs and unit disk graphs. They can be extended to intersections graphs of other "disklike" geometric objects (such as squares or regular polygons), also in higher dimensions.
On spectrum sharing games
 In proc. of PODC 2004
, 2004
"... Each access point (AP) in a WiFi network must be assigned a channel for it to service users. There are only finitely many possible channels that can be assigned. Moreover, neighboring access points must use different channels so as to avoid interference. Currently these channels are assigned by admi ..."
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Cited by 78 (3 self)
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Each access point (AP) in a WiFi network must be assigned a channel for it to service users. There are only finitely many possible channels that can be assigned. Moreover, neighboring access points must use different channels so as to avoid interference. Currently these channels are assigned by administrators who carefully consider channel conflicts and network loads. Channel conflicts among APs operated by different entities are currently resolved in an ad hoc manner or not resolved at all. We view the channel assignment problem as a game, where the players are the service providers and APs are acquired sequentially. We consider the price of anarchy of this game, which is the ratio between the total coverage of the APs in the worst Nash equilibrium of the game and what the total coverage of the APs would be if the channel assignment were done by a central authority. We provide bounds on the price of anarchy depending on assumptions on the underlying network and the type of bargaining allowed between service providers. The key tool in the analysis is the identification of the Nash equilibria with the solutions to a maximal coloring problem in an appropriate graph. We relate the price of anarchy of these games to the approximation factor of local optimization algorithms for the maximum�colorable subgraph problem. We also study the speed of convergence in these games.
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.
A PTAS for the minimum dominating set problem in unit disk graphs
 In WAOA
, 2005
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Algorithms For Graphs Embeddable With Few Crossings Per Edge
 PROC. 15TH INT. SYMP. ON FUNDAMENTALS OF COMPUTATION THEORY (FCT’05), VOLUME 3623 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2004
"... We consider graphs that can be embedded on a surface of bounded genus such that each edge has a bounded number of crossings. We prove that many optimization problems, including maximum independent set, minimum vertex cover, minimum dominating set and many others, admit polynomial time approximati ..."
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Cited by 13 (0 self)
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We consider graphs that can be embedded on a surface of bounded genus such that each edge has a bounded number of crossings. We prove that many optimization problems, including maximum independent set, minimum vertex cover, minimum dominating set and many others, admit polynomial time approximation schemes when restricted to such graphs. This extends previous results by Baker [1] and Eppstein [7] to a much broader class of graphs. We also show that testing if a graph can be drawn in the plane with at most one crossing per edge is NPcomplete.
Independent and Dominating Sets in Wireless Communication Graphs
, 2006
"... any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without the prior written permission of the author. Printed by Wöhrmann Print Service. ..."
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Cited by 8 (1 self)
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any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without the prior written permission of the author. Printed by Wöhrmann Print Service.
Wireless communication graphs
 In Intelligent Sensors, Sensor Networks and Information Processing Conference (ISSNIP
, 2004
"... This thesis was edited with NEdit and typeset with L ATEX2e. ..."
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Cited by 4 (2 self)
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This thesis was edited with NEdit and typeset with L ATEX2e.
Approximating Minimum Independent Dominating Sets in Wireless Networks
"... We present the first polynomialtime approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded growth are used to characterize wireless communication networks, and this class of graph includes many models known from the ..."
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Cited by 1 (0 self)
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We present the first polynomialtime approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded growth are used to characterize wireless communication networks, and this class of graph includes many models known from the literature, e.g. (Quasi) Unit Disk Graphs. An independent dominating set is a dominating set in a graph that is also independent. It thus combines the advantages of both structures, and there are many applications that rely on these two structures e.g. in the area of wireless ad hoc networks. The presented approach yields a robust algorithm, that is, the algorithm accepts any undirected graph as input, and returns a (1+ε)approximate minimum dominating set, or a certificate showing that the input graph does not reflect a wireless network.
DREAM: On the Reaction Delay in Large Scale Wireless Networks with Mobile Sensors
"... Abstract—In this work, we present a monitor and rescue system utilizing hybrid networks which is a integration of stationary sensor networks and mobile sensor networks: stationary sensor networks comprised of large numbers of small, simple, and inexpensive wireless sensors, and the mobile sensor net ..."
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Abstract—In this work, we present a monitor and rescue system utilizing hybrid networks which is a integration of stationary sensor networks and mobile sensor networks: stationary sensor networks comprised of large numbers of small, simple, and inexpensive wireless sensors, and the mobile sensor network contains a set of mobile sensors (robots). The static sensors in our network have “monitoring ” ability, i.e., any activated static sensor can detect the event as long as its sensing range intersects the event region. And the mobile sensors have “moving ” and “rescuing” ability, e.g., they can move toward the event region with limited speed and further perform certain rescuing/processing operations on the event. We can consider the event as a hazard, e.g., wild fire, and the mobile sensors as fireman robots. As soon as the fire is detected by the static sensors, the fireman robots are expected to move from its initial location to the hazard region within minimum latency. We define the reaction delay of the system as the delay from the occurrence of event till at least one mobile sensor reaches the event. In order to satisfy certain reaction delay requirement while minimizing the total cost, we propose a number of deployment strategies for the stationary sensor network and mobile sensor network respectively. We further design a random wakeup scheduling for the static sensors for the sake of energy efficiency. Finally, we propose a pure distributed motion strategy for mobile sensors without reliance on localization services such as GPS, focusing on simple algorithms for distributed decision making and information propagation. We demonstrate the efficacy of our system in simulation, providing empirical results. KeywordsSensor networks, mobility, detection, delay. I.