Graph Imperfection

Gerke, Stefanie; McDiarmid, Colin

doi:10.1006/jctb.2001.2042

Cited by 54 publications

(73 citation statements)

References 27 publications

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“…This quantity has been studied in [9]; it is finite and is achieved for any given graph. In the definition above, for a given demand vector τ , the numerator specifies the exact amount of resource required to satisfy the demand, as determined by an optimal, centralized algorithm.…”

Section: Clique Constraintsmentioning

confidence: 99%

“…The following general result is implicit in [11] (where the authors focus on unit disk graphs) and in [9]: Proposition 11. The largest scaling factor which converts the necessary clique constraints into a sufficient condition is 1/ imp(G C ); i.e.…”

Section: Clique Constraintsmentioning

confidence: 99%

“…The problem of determining the imperfection ratio of various families of graphs has been studied in [9].…”

Section: Clique Constraintsmentioning

confidence: 99%

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Performance of sufficient conditions for distributed quality-of-service support in wireless networks

Ganesan

2013

Wireless Netw

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Given a wireless network where some pairs of communication links interfere with each other, we study sufficient conditions for determining whether a given set of minimum bandwidth quality-of-service (QoS) requirements can be satisfied. We are especially interested in algorithms which have low communication overhead and low processing complexity. The interference in the network is modeled using a conflict graph whose vertices correspond to the communication links in the network. Two links are adjacent in this graph if and only if they interfere with each other due to being in the same vicinity and hence cannot be simultaneously active. The problem of scheduling the transmission of the various links is then essentially a fractional, weighted vertex coloring problem, for which upper bounds on the fractional chromatic number are sought using only localized information. We recall some distributed algorithms for this problem, and then assess their worst-case performance. Our results on this fundamental problem imply that for some well known classes of networks and interference models, the performance of these distributed algorithms is within a bounded factor away from that of an optimal, centralized algorithm. The performance bounds are simple expressions in terms of graph invariants. It is seen that the induced star number of a network plays an important role in the design and performance of such networks.Index terms -flow admission control, quality-of-service (QoS), distributed algorithms, interference, wireless networks, conflict graph, link scheduling; fractional chromatic number; induced star number. IntroductionIn recent years there has been an increasing interest in using data networks to support a wide variety of applications, each requiring a different Quality-of-Service (QoS). For example, real-time applications such as voice, video and industrial control are time-sensitive and require that the delay be small, while for other data applications the sender may require that a constant, minimum bit-rate service be provided. In the simplest and lowest level of service, such as the one provided in the Internet Protocol service model, the network makes a best-effort to deliver data from the source to destination, but it makes no guarantees of any kind, so it is possible that packets can get dropped, delayed, or delivered out of order. However, this basic level of service is insufficient for many data applications such as * This work was carried out while the author was with the ECE Department, University of Wisconsin at Madison, WI 53706, USA. This work was presented in part at the International Conference on Networks and Communications (GraphHoc and NetCoM), Chennai, India, December 2009 [5], and at the International Conference on Recent Trends in Graph Theory and Combinatorics (an ICM Satellite Conference), Cochin, India, August 2010 [6]. This paper is a revised version of the Technical Report [8]. The author is with the Department of Mathematics, Amrita School of Engineering, Amrita University, Coimbato...

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Section: Clique Constraintsmentioning

confidence: 99%

Section: Clique Constraintsmentioning

confidence: 99%

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Performance of sufficient conditions for distributed quality-of-service support in wireless networks

Ganesan

2013

Wireless Netw

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“…The proof can be found in [18]. The scaling factor α is defined as α = 1/imp(CG), where imp(CG) is the imperfection ratio [19] of the conflict graph CG. If CG is a unit disk graph, [19] shows that imp(CG) ≤ 2.155.…”

Section: Feasibility Conditions Of Flowsmentioning

confidence: 99%

“…The scaling factor α is defined as α = 1/imp(CG), where imp(CG) is the imperfection ratio [19] of the conflict graph CG. If CG is a unit disk graph, [19] shows that imp(CG) ≤ 2.155. This corresponds to the case where the nodes of the ad-hoc network are placed on the ground of a free space with no obstacles in between, and the scaling factor is α = 1 2.155 ≈ 0.46.…”

Section: Feasibility Conditions Of Flowsmentioning

confidence: 99%

Bandwidth Guaranteed Routing for Ad Hoc Networks with Interference Consideration

Jia¹,

Gupta²,

Walrand³

et al.

10th IEEE Symposium on Computers and Communications (ISCC'05)

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Abstract-The problem of computing bandwidth guaranteed paths for given flow requests in an ad-hoc network is complicated because neighboring links share the medium. We define the path width on top of the conflict graph based interference model, and present the Ad-Hoc Shortest Widest Path (ASWP) routing problem in an adhoc network context. We propose a distributed algorithm to address the ASWP problem. Adopting the BellmanFord architecture and the k-shortest-path approach, the proposed algorithm achieves a performance close to the optimum. Numerical simulations demonstrate the performance of the algorithm, and also analyze gains achieved over prevalent shortest-path algorithms.

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Channel assignment and weighted coloring

2000

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In cellular telephone networks, sets of radio channels (colors) must be assigned to transmitters (vertices) while avoiding interference. Often, the transmitters are laid out like vertices of a triangular lattice in the plane. We investigated the corresponding weighted coloring problem of assigning sets of colors to vertices of the triangular lattice so that the sets of colors assigned to adjacent vertices are disjoint. We present a hardness result and an efficient algorithm yielding an approximate solution.

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Graph Imperfection

Cited by 54 publications

References 27 publications

Performance of sufficient conditions for distributed quality-of-service support in wireless networks

Performance of sufficient conditions for distributed quality-of-service support in wireless networks

Bandwidth Guaranteed Routing for Ad Hoc Networks with Interference Consideration

Channel assignment and weighted coloring

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