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147
NCApproximation Schemes for NP and PSPACEHard Problems for Geometric Graphs
, 1997
"... We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance tradeoff as the best known approximation schemes for planar gr ..."
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Cited by 119 (1 self)
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We present NC approximation schemes for a number of graph problems when restricted to geometric graphs including unit disk graphs and graphs drawn in a civilized manner. Our approximation schemes exhibit the same time versus performance tradeoff as the best known approximation schemes for planar graphs. We also define the concept of precision unit disk graphs and show that for such graphs the approximation schemes have a better time versus performance tradeoff than the approximation schemes for arbitrary unit disk graphs. Moreover, compared to unit disk graphs, we show that for precision unit disk graphs, many more graph problems have efficient approximation schemes. Our NC approximation schemes can also be extended to obtain efficient NC approximation schemes for several PSPACEhard problems on unit disk graphs specified using a restricted version of the hierarchical specification language of Bentley, Ottmann and Widmayer. The approximation schemes for hierarchically specified un...
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 87 (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.
Minimizing broadcast latency and redundancy in ad hoc networks
 In Proc. of the Fourth ACM Int. Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC'03
, 2003
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Models and Approximation Algorithms for Channel Assignment in Radio Networks
, 2000
"... We consider the frequency assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with a certain geometric structure. The problem of broadcast scheduling can be cast as a variant of the vertex coloring problem (called the distance2 coloring ..."
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Cited by 80 (3 self)
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We consider the frequency assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with a certain geometric structure. The problem of broadcast scheduling can be cast as a variant of the vertex coloring problem (called the distance2 coloring problem) on the graph that models a given packet radio network. We present efficient approximation algorithms for the distance2 coloring problem for various geometric graphs including those that naturally model a large class of packet radio networks. The class of graphs considered include (r, s)civilized graphs, planar graphs, graphs with bounded genus, etc.
Allocating Dynamic TimeSpectrum Blocks In Cognitive Radio Networks
, 2007
"... A number of studies have shown the abundance of unused spectrum in the TV bands. This is in stark contrast to the overcrowding of wireless devices in the ISM bands. A recent trend to alleviate this disparity is the design of Cognitive Radios, which constantly sense the spectrum and opportunistically ..."
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Cited by 77 (2 self)
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A number of studies have shown the abundance of unused spectrum in the TV bands. This is in stark contrast to the overcrowding of wireless devices in the ISM bands. A recent trend to alleviate this disparity is the design of Cognitive Radios, which constantly sense the spectrum and opportunistically utilize unused frequencies in the TV bands. In this paper, we introduce the concept of a timespectrum block to model spectrum reservation, and use it to present a theoretical formalization of the spectrum allocation problem in cognitive radio networks. We present a centralized and a distributed protocol for spectrum allocation and show that these protocols are close to optimal in most scenarios. We have implemented the distributed protocol in QualNet and show that our analysis closely matches the simulation results.
Label Placement by Maximum Independent Set in Rectangles
 Computational Geometry: Theory and Applications
, 1997
"... Motivated by the problem of labeling maps, we investigate the problem of computing a large nonintersecting subset in a set of n rectangles in the plane. Our results are as follows. In O(n log n) time, we can find an O(log n)factor approximation of the maximum subset in a set of n arbitrary axispa ..."
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Cited by 77 (5 self)
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Motivated by the problem of labeling maps, we investigate the problem of computing a large nonintersecting subset in a set of n rectangles in the plane. Our results are as follows. In O(n log n) time, we can find an O(log n)factor approximation of the maximum subset in a set of n arbitrary axisparallel rectangles in the plane. If all rectangles have unit height, we can find a 2approximation in O(n log n) time. Extending this result, we obtain a (1 + 1 k )approximation in time O(n log n + n 2k\Gamma1 ) time, for any integer k 1. 1 Introduction Automated label placement is an important problem in geographic information systems (GIS), and has received considerable attention in recent years (for instance, see [6, 9]). The label placement problem includes positioning labels for area, line, and point features. The primary focus within the computational geometry community has been on labeling point features [5, 7, 17, 16]. A basic requirement in the label placement problem is that ...
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 76 (1 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.
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 76 (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.
On the Maximum Stable Throughput Problem in Random Networks with Directional Antennas
 IN PROC. ACM MOBIHOC
, 2003
"... We consider the problem of determining rates of growth for the maximum stable throughput achievable in dense wireless networks. We formulate this problem as one of finding maximum flows on random unitdisk graphs. Equipped with the maxflow/mincut theorem as our basic analysis tool, we obtain rates ..."
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Cited by 66 (8 self)
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We consider the problem of determining rates of growth for the maximum stable throughput achievable in dense wireless networks. We formulate this problem as one of finding maximum flows on random unitdisk graphs. Equipped with the maxflow/mincut theorem as our basic analysis tool, we obtain rates of growth under three models of communication: (a) omnidirectional transmissions; (b) "simple" directional transmissions, in which sending nodes generate a single beam aimed at a particular receiver; and (c) "complex " directional transmissions, in which sending nodes generate multiple beams aimed at multiple receivers. Our main finding is that an increase of 54 54 in maximum stable throughput is all that can be achieved by allowing arbitrarily complex signal processing (in the form of generation of directed beams) at the transmitters and receivers. We conclude therefore that neither directional antennas, nor the ability to communicate simultaneously with multiple nodes, can be expected in practice to effectively circumvent the constriction on capacity in dense networks that results from the geometric layout of nodes in space.
Forwardnodesetbased broadcast in clustered mobile ad hoc networks
 Wireless Communication and Mobile Computing
, 2003
"... A taxonomy of broadcast protocols in mobile ad hoc networks (MANETs) is given where protocols are classified into four groups: global, quasiglobal, quasilocal, and local. The taxonomy also divides protocols based on the nature of algorithms: probabilistic and deterministic. The locality of mainten ..."
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Cited by 58 (14 self)
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A taxonomy of broadcast protocols in mobile ad hoc networks (MANETs) is given where protocols are classified into four groups: global, quasiglobal, quasilocal, and local. The taxonomy also divides protocols based on the nature of algorithms: probabilistic and deterministic. The locality of maintenance also plays an important role in evaluating the protocol. An important objective in designing a broadcast protocol is to reduce broadcast redundancy to save scarce resources such as energy and bandwidth and to avoid the broadcast storm problem. This objective should be achieved without introducing excessive overhead and time delay, measured by the sequential rounds of information exchanges. This is done by choosing a small forward node set that forms a connected dominating set (CDS) to carry out a broadcast process. In this paper, a clustered network model is proposed in which each node is a clusterhead in the clustered architecture. Clusterheads are connected by carefully selecting nonclusterhead nodes locally at each clusterhead to connect clusterheads within 2.5 hops, a novel notion proposed in this paper. Information of neighbor clusterheads are piggybacked with the broadcast packet to further reduce each forward node set. It is shown that this approach is quasilocal with locality of maintenance. In addition, this approach has a constant approximation ratio to the minimum connected dominating set (MCDS) and generates a small forward node set in the average case. Comparisons are also done through simulation with representative protocols from each of the four groups of protocols based on the proposed taxonomy.