New Graph Coloring Algorithms

Al-Omari, Hussein; Sabri, Khair Eddin

doi:10.3844/jmssp.2006.439.441

Cited by 32 publications

(29 citation statements)

References 1 publication

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“…Among these heuristics, First-Fit and Degree-Based Ordering are among the best-known solutions [2]. Algorithm 1 presents the most general form of the First-Fit Vertex Coloring Algorithm.…”

Section: Olsr-aware Centralized Channel Access Schedulingmentioning

confidence: 99%

“…In the First-Fit Vertex Coloring Algorithm, no particular strategy is applied for the selection order of the nodes to be colored. On the other hand, in the Maximum Degree First (MDF) Vertex Coloring Algorithm, the vertex with the highest number of neighbors is selected first, providing an intuitively better coloring than the First-Fit Vertex Coloring Algorithm [2]. On the other hand, distance-d coloring is a special form of vertex coloring.…”

Section: Olsr-aware Centralized Channel Access Schedulingmentioning

confidence: 99%

“…NOA-C makes use of the above-mentioned Distance-2 Maximum Degree First heuristic which is widely used/extended in many studies [2,38]. In Algorithm 4, we present a high-level description of how we implement this algorithm in our framework so that a fair comparison of the scheduling schemes discussed (OA-C and NOA-C) is possible.…”

Section: Olsr-aware Centralized Channel Access Schedulingmentioning

confidence: 99%

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OLSR-aware channel access scheduling in wireless mesh networks

Kas

Korpeoglu

Karasan

2011

Journal of Parallel and Distributed Computing

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a b s t r a c tWireless mesh networks (WMNs) have emerged as a key technology having various advantages, especially in providing cost-effective coverage and connectivity solutions in both rural and urban areas. WMNs are typically deployed as backbone networks, usually employing spatial TDMA (STDMA)-based access schemes which are suitable for the high traffic demands of WMNs. This paper aims to achieve higher utilization of the network capacity and thereby aims to increase the application layer throughput of STDMA-based WMNs. The central idea is to use optimized link state routing (OLSR)-specific routing layer information in link layer channel access schedule formation. This paper proposes two STDMAbased channel access scheduling schemes (one distributed, one centralized) that exploit OLSR-specific information to improve the application layer throughput without introducing any additional messaging overhead. To justify the contribution of using OLSR-specific information to the throughput, the proposed schemes are compared against one another and against their non-OLSR-aware versions via extensive ns-2 simulations. Our simulation results verify that utilizing OLSR-specific information significantly improves the overall network performance both in distributed and in centralized schemes. The simulation results further show that OLSR-aware scheduling algorithms attain higher end-to-end throughput although their non-OLSR-aware counterparts achieve higher concurrency in slot allocations.

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“…Among these heuristics, First-Fit and Degree-Based Ordering are among the best-known solutions [2]. Algorithm 1 presents the most general form of the First-Fit Vertex Coloring Algorithm.…”

Section: Olsr-aware Centralized Channel Access Schedulingmentioning

confidence: 99%

Section: Olsr-aware Centralized Channel Access Schedulingmentioning

confidence: 99%

Section: Olsr-aware Centralized Channel Access Schedulingmentioning

confidence: 99%

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OLSR-aware channel access scheduling in wireless mesh networks

Kas

Korpeoglu

Karasan

2011

Journal of Parallel and Distributed Computing

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“…While this strategy is simple to implement, computing a column grouping of minimal size is well known to be an NP-hard problem-this problem corresponds precisely to the graph coloring problem [5,6]. There are, however, efficient algorithms capable of computing practically useful approximations of the optimal solutions.…”

Section: Exploiting Sparsitymentioning

confidence: 99%

Generation of Sparse Jacobians for the Function Mock-Up Interface 2.0

Åkesson¹,

Braun²,

Lindholm³

et al. 2012

Linköping Electronic Conference Proceedings

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Derivatives, or Jacobians, are commonly required by numerical algorithms. Access to accurate Jacobians often improves the performance and robustness of algorithms, and in addition, efficient implementation of Jacobian computations can reduce the over-all execution time. In this paper, we present methods for computing Jacobians in the context of the Functional Mock-up Interface (FMI), and Modelica. Two prototype implementations, in JModelica.org and OpenModelica are presented and compared in industrial as well as synthetic benchmarks.

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“…The greedy algorithms generally provide effective and sufficient results for vertex coloring [15]. In this study, we described First Fit (FF) [19], Largest Degree Ordering (LDO) [19], Welsh and Powell (WP) [5], Incidence Degree Ordering (IDO) [19], Recursive Largest First (RLF) [20] and Degree of Saturation (DSATUR) [21] algorithms which have been proposed in the literature for the vertex coloring problem and these algorithms were tested on benchmark graphs provided by DIMACS [22]. The performances of the algorithms were compared with each other in terms of their solution qualities and executing times.…”

Section: Introductionmentioning

confidence: 99%

A Performance Comparison of Graph Coloring Algorithms

ASLAN¹

2016

ijisae

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Graph coloring problem (GCP) is getting more popular to solve the problem of coloring the adjacent regions in a map with minimum different number of colors. It is used to solve a variety of real-world problems like map coloring, timetabling and scheduling. Graph coloring is associated with two types of coloring as vertex and edge coloring. The goal of the both types of coloring is to color the whole graph without conflicts. Therefore, adjacent vertices or adjacent edges must be colored with different colors. The number of the least possible colors to be used for GCP is called chromatic number. As the number of vertices or edges in a graph increases, the complexity of the problem also increases. Because of this, each algorithm can not find the chromatic number of the problems and may also be different in their executing times. Due to these constructions, GCP is known an NP-hard problem. Various heuristic and metaheuristic methods have been developed in order to solve the GCP. In this study, we described First Fit (FF), Largest Degree Ordering (LDO), Welsh and Powell (WP), Incidence Degree Ordering (IDO), Degree of Saturation (DSATUR) and Recursive Largest First (RLF) algorithms which have been proposed in the literature for the vertex coloring problem and these algorithms were tested on benchmark graphs provided by DIMACS. The performances of the algorithms were compared as their solution qualities and executing times. Experimental results show that while RLF and DSATUR algorithms are sufficient for the GCP, FF algorithm is generally deficient. WP algorithm finds out the best solution in the shortest time on Register Allocation, CAR, Mycielski, Stanford Miles, Book and Game graphs. On the other hand, RLF algorithm is quite better than the other algorithms on Leighton, Flat, Random (DSJC) and Stanford Queen graphs.

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New Graph Coloring Algorithms

Cited by 32 publications

References 1 publication

OLSR-aware channel access scheduling in wireless mesh networks

OLSR-aware channel access scheduling in wireless mesh networks

Generation of Sparse Jacobians for the Function Mock-Up Interface 2.0

A Performance Comparison of Graph Coloring Algorithms

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