Smallest-last ordering and clustering and graph coloring algorithms

Matula, David W.; Beck, Leland L.

doi:10.1145/2402.322385

Cited by 423 publications

(218 citation statements)

References 11 publications

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“…Recently, weakenings of hierarchies are also increasingly studied. They include hierarchies of packings [91], weak hierarchies [2] and pyramids [35]. Work has also been done on fuzzy clustering, in which entities have a degree of membership in one or several clusters [10].…”

Section: Types Of Clusteringmentioning

confidence: 99%

“…Some clustering algorithms apply to graphs, which may be viewed as partial graphs G t as defined above, for a given t. Clusters may then be defined as maximal components with minimum degree at least δ [91]; a O(N + |E|) algorithm provides a hierarchy of packings corresponding to successive values of δ. When clustering points in R 2 , geometric properties may be exploited to obtain low-order polynomial algorithms.…”

Section: Colorable Then the Color Classes In Any Optimal Coloring Ofmentioning

confidence: 99%

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Cluster analysis and mathematical programming

Hansen

Jaumard

1997

Mathematical Programming

413

251

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Les textes publiés dans la série des rapports de recherche HEC n'engagent que la responsabilité de leurs auteurs. La publication de ces rapports de recherche bénéficie d'une subvention du Fonds F.C.A.R. Cluster Analysis and Mathematical ProgrammingPierre Hansen GERAD andÉcole des HautesÉtudes Commerciales Montréal, CanadaBrigitte Jaumard GERAD andÉcole Polytechnique de Montréal Canada February, 1997Les Cahiers du GERAD G-97-10Abstract Given a set of entities, Cluster Analysis aims at finding subsets, called clusters, which are homogeneous and/or well separated. As many types of clustering and criteria for homogeneity or separation are of interest, this is a vast field. A survey is given from a mathematical programming viewpoint.Steps of a clustering study, types of clustering and criteria are discussed. Then algorithms for hierarchical, partitioning, sequential, and additive clustering are studied. Emphasis is on solution methods, i.e., dynamic programming, graph theoretical algorithms, branch-and-bound, cutting planes, column generation and heuristics.

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Section: Types Of Clusteringmentioning

confidence: 99%

Section: Colorable Then the Color Classes In Any Optimal Coloring Ofmentioning

confidence: 99%

Cluster analysis and mathematical programming

Hansen

Jaumard

1997

Mathematical Programming

413

251

View full text Add to dashboard Cite

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“…It can be readily seen that the underlying resource allocation subproblem associated with a given user-centric cluster formation can be translated to a graph coloring problem, but this graph coloring problem cannot be solved directly by the existing graph-based techniques. However, we emphasize that the basic ideas of random coloring and sequential coloring [46] are widely adopted in various resource allocation problems for comparison, such as in [19] [47] [48] and [24], respectively. Hence, we can exploit the basic ideas of random coloring and sequential coloring in our user-centric resource allocation subproblem based on usercentric overlapped clustering UDNs.…”

Section: User-centric Resource Allocation Solutionmentioning

confidence: 99%

Graph-Based Joint User-Centric Overlapped Clustering and Resource Allocation in Ultradense Networks

Lin

Zhang

et al. 2018

IEEE Trans. Veh. Technol.

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Abstract-With the increase of access point (AP) density and the exponential growth of mobile devices supported by ultra dense networks (UDNs), user-centric overlapped clustering relying on AP cooperation is becoming a promising design principle for guaranteeing the quality of service (QoS) required by each UE. This ambitious goal can be achieved by the joint design of user-centric overlapped clustering and resource allocation. In this context, both the traffic-load balancing and the limited availability of orthogonal resource blocks (RBs) have to be carefully considered in UDNs. To tackle these challenges, we formulate a joint user-centric overlapped clustering and resource allocation problem with the goal of maximizing the system's spectral efficiency (SE). To efficiently solve this problem, it is decoupled into two subproblems, which can be solved independently with the aid of our graph-theoretical framework. We first develop a novel distributed three-stage user-centric clustering solution, which is aware of the APs' traffic-loads. Then, based on the overlapped clusters constructed, we propose a novel two-stage graph-based user-centric resource allocation scheme for mitigating the resultant inter-cluster interference, despite the limited availability of orthogonal RBs. Our numerical results confirm the benefits of the proposed framework and show that it outperforms the benchmark solutions in terms of both its per area aggregated user rate (PAAR) and user rate.

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“…Finding a feasible schedule is equivalent to finding a proper k-coloring of the corresponding interval graph, such that no two adjacent vertices can have the same color (overlapping jobs are assigned to different servers). Interval graphs and graph coloring problems have been studied intensively in the literature (see [5,6] and references within).…”

Section: Definitionsmentioning

confidence: 99%

“…The SLV heuristic algorithm orders the vertices of the interval graph according to the smallest-last ordering [5]. The vertices v 1 , v 2 , .…”

Section: Smallest-last Vertex Ordering (Slv)mentioning

confidence: 99%

Batch Scheduling Algorithms for Optical Burst Switching Networks

Kaheel

Alnuweiri

2005

NETWORKING 2005. Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile A

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Abstract. Previously proposed wavelength scheduling algorithms in optical burst switching networks process each reservation request individually and in a greedy manner. In this paper we propose a new family of wavelength scheduling algorithms that process a batch of reservation requests together instead of processing them one by one. When a control burst with a reservation request arrives to a free batch scheduler, the scheduler waits for a small amount of time, called the acceptance delay, before deciding to accept or reject the reservation request. After the acceptance delay has passed, the scheduler processes all the reservation requests that have arrived during the acceptance delay, then it accepts the requests that will maximize the utilization of the wavelength channels. We describe an optimal batch scheduler that serves as an upper bound on the performance of batch scheduling algorithms. Furthermore, we introduce two heuristic batch scheduling algorithms. The performance of the proposed algorithms is evaluated using a discrete-event simulation model. Simulation results suggest that batch schedulers could decrease the blocking probability by 25% compared to the best previously known wavelength scheduling algorithm.

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Smallest-last ordering and clustering and graph coloring algorithms

Cited by 423 publications

References 11 publications

Cluster analysis and mathematical programming

Cluster analysis and mathematical programming

Graph-Based Joint User-Centric Overlapped Clustering and Resource Allocation in Ultradense Networks

Batch Scheduling Algorithms for Optical Burst Switching Networks

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