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27
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 72 (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 40 (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.
Approximation Algorithms for Channel Assignment in Radio Networks
 Wireless Networks
, 1998
"... We consider the channel assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with certain geometric structure. The channel assignment problem can be cast as a variant of the vertex coloring problem (called the distance2 coloring problem) ..."
Abstract

Cited by 24 (1 self)
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We consider the channel assignment (broadcast scheduling) problem for packet radio networks. Such networks are naturally modeled by graphs with certain geometric structure. The channel assignment problem 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 several classes of graphs including a class of geometric graphs that naturally model a large class of packet radio networks. The classes of graphs considered include (r, s)civilized graphs, planar graphs, graphs with bounded genus, etc. Many of the approximation results presented here are the first such results in the literature.
Sufficient Rate Constraints for QoS Flows in AdHoc Networks
"... The capacity of an arbitrary adhoc network is difficult to estimate due to interference between the links. We use a conflict graph that models this interference relationship to determine if a set of flow rates can be accommodated. Using the cliques (complete subgraphs) of the conflict graph, we der ..."
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Cited by 21 (4 self)
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The capacity of an arbitrary adhoc network is difficult to estimate due to interference between the links. We use a conflict graph that models this interference relationship to determine if a set of flow rates can be accommodated. Using the cliques (complete subgraphs) of the conflict graph, we derive constraints that are sufficient for a set of flow rates to be feasible, yet are guaranteed to be within a constant bound of the optimal. We also compute an alternate set of sufficient constraints that can be easily derived from the rows of the matrix representation of the conflict graph. These two sets of constraints are particularly useful because their construction and verification may be distributed across the nodes of a network. We also extend the adhoc network model to incorporate variations in the interference range, and obstructions in the network.
Simple Heuristics and PTASs for Intersection Graphs in Wireless Ad Hoc Networks
 in Wireless Ad Hoc Networks, in DialM’02
, 2002
"... In wireless ad hoc networks, each wireless device has a transmission range, which is usually modeled as a disk centered at this node. A wireless node can send message directly to all nodes lying inside this disk. We present several intersection graphs to model the wireless networks. Then we present ..."
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Cited by 18 (8 self)
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In wireless ad hoc networks, each wireless device has a transmission range, which is usually modeled as a disk centered at this node. A wireless node can send message directly to all nodes lying inside this disk. We present several intersection graphs to model the wireless networks. Then we present some simple heuristics and/or PTASs to approximate the maximum independent set, the minimum vertex cover and the minimum graph coloring in these graph models.
MiFi: A Framework for Fairness and QoS Assurance in Current IEEE 802.11 Networks with Multiple Access Points
, 2004
"... In this paper we present a framework for providing fair service and supporting QoS requirements in IEEE 802.11 networks with multiple accesspoints (APs). These issues becomes critical as IEEE 802.11 wireless LAN are widely deployed in nationwide networks, linking tens of thousands of "hotspots" fo ..."
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Cited by 15 (0 self)
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In this paper we present a framework for providing fair service and supporting QoS requirements in IEEE 802.11 networks with multiple accesspoints (APs). These issues becomes critical as IEEE 802.11 wireless LAN are widely deployed in nationwide networks, linking tens of thousands of "hotspots" for providing both realtime (voice) and non realtime (data) services to a large population of mobile users. However, both fairness and QoS guarantees cannot be supported in the current 802.11 standard.
Approximating Maximal Cliques in AdHoc Networks
 IN PROC. IEEE PERSONAL, INDOOR, AND MOBILE RADIO COMMUNICATIONS CONFERENCE (PIMRC
, 2004
"... The capacity of an adhoc network is severely affected by interference between links, and several efforts to model this effect make use of ‘clique ’ structures in the adhoc graphs. We propose a fully distributed heuristic algorithm to approximate cliques in such networks. We further propose methods ..."
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Cited by 13 (1 self)
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The capacity of an adhoc network is severely affected by interference between links, and several efforts to model this effect make use of ‘clique ’ structures in the adhoc graphs. We propose a fully distributed heuristic algorithm to approximate cliques in such networks. We further propose methods to shrink the generated set of cliques to a set of maximal cliques. Simulation results verify the efficacy of the heuristic algorithms and also analyze their computation time.
Independence and Coloring Problems on Intersection Graphs of Disks
, 2001
"... This paper surveys online and approximation algorithms for the maximum independent set and coloring problems on intersection graphs of disks. As a new result, it is shown that no deterministic online algorithm can achieve competitive ratio better than (log n) for disk graphs and for square g ..."
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Cited by 7 (2 self)
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This paper surveys online and approximation algorithms for the maximum independent set and coloring problems on intersection graphs of disks. As a new result, it is shown that no deterministic online algorithm can achieve competitive ratio better than (log n) for disk graphs and for square graphs with n vertices, even if the geometric representation is given as part of the input. Furthermore, it is proved that the standard First t heuristic achieves competitive ratio O(log n) for disk graphs and for square graphs and is thus best possible.
GRAPH COLOURING PROBLEMS AND THEIR APPLICATIONS IN SCHEDULING
, 2003
"... Graph colouring and its generalizations are useful tools in modelling a wide variety of scheduling and assignment problems. In this paper we review several variants of graph colouring, such as precolouring extension, list colouring, multicolouring, minimum sum colouring, and discuss their applicatio ..."
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Cited by 7 (0 self)
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Graph colouring and its generalizations are useful tools in modelling a wide variety of scheduling and assignment problems. In this paper we review several variants of graph colouring, such as precolouring extension, list colouring, multicolouring, minimum sum colouring, and discuss their applications in scheduling.
On the chromatic number of random geometric graphs
 Combinatorica
"... Given independent random points X1,..., Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n)> 0, we construct a random geometric graph Gn with vertex set {1,..., n} where distinct i and j are adjacent when ‖Xi − Xj ‖ ≤ r. Here ‖. ‖ may be any norm on Rd, and ν may be any ..."
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Cited by 7 (3 self)
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Given independent random points X1,..., Xn ∈ Rd with common probability distribution ν, and a positive distance r = r(n)> 0, we construct a random geometric graph Gn with vertex set {1,..., n} where distinct i and j are adjacent when ‖Xi − Xj ‖ ≤ r. Here ‖. ‖ may be any norm on Rd, and ν may be any probability distribution on Rd with a bounded density function. We consider the chromatic number χ(Gn) of Gn and its relation to the clique number ω(Gn) as n → ∞. Both McDiarmid [11] ln n and Penrose [15] considered the range of r when r ≪ ( n)1/d and the range when ln n r ≫ ( n)1/d, and their results showed a dramatic difference between these two cases. Here we sharpen and extend the earlier results, and in particular we consider t ln n