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Without loss of generality, we assume the following:. For each element e i of e, two fields e i. Thus, the fields e i.

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For the graph of Figure 1 , the array e is shown in the Table 1. Table 1. To find the disjoint cliques on interval graphs, we have to first compute all maximal cliques and the time complexity of which given in the following lemma. One more important characterization of the interval graph with respect to cliques is given by Gilmore and Hoffman [ 18 ].

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It is stated as follows:. A graph G is an interval graph if and only if the maximal cliques of G can be linearly ordered in such a way that for every vertex v of G, the maximal cliques containing v occur consecutively [ 18 ]. Using Lemma-1, we can determine all maximal cliques. If p u is the largest subscript of the maximal cliques in which u belongs, then we call the clique C p u as end clique of u, i. From Lemma-2, we have. As it. Hence, any one among. This means the graph G is disconnected. The array FirstDisjoint plays an important role for construction of the network N.

An algorithm to compute this array is presented below:. Theorem-1 : Algorithm FD can be computed in n 2 time in sequential. Similarly, Step-3 and Step-4 takes n 2 time. Therefore, overall time complexity of the Algorithm FD is of n 2. Hence the theorem. The network N has also a. A path having maximum total weight among all paths from A 0 to A m is called the maximum weight path. Proceedings of the Steklov Institute of Mathematics :S1, Autonomous Agents and Multi-Agent Systems 22 :2, Flows in Networks.

Graphs: Theory and Algorithms, Journal of Scheduling 14 :1, Artificial Intelligence :2, International Journal of Communication Systems 24 :2, Discrete Applied Mathematics :1, Journal of Combinatorial Optimization 21 :1, Over-Constrained Problems. Hybrid Optimization, Theoretical Computer Science, Automata, Languages and Programming, Integer Programming and Combinatoral Optimization, Optical Supercomputing, Algorithms and Data Structures, Algorithms — ESA , Matching Massimo.

Ottimizzazione Combinatoria, Acta Automatica Sinica 36 , Performance evaluation. Video Tracking, Multi-target management. Flexible Services and Manufacturing Journal 22 , Discrete Mathematics, Algorithms and Applications 02 , Algorithmica 58 :1, Constraints 15 :3, Discrete Mathematics :9, Journal of Biomolecular NMR 46 :4, Pattern Recognition 43 :3, Algorithmica 56 :3, Theoretical Computer Science :6, Flavio Chierichetti and Andrea Vattani. Managing and Mining Graph Data, Fundamental Approaches to Software Engineering, Couplage maximum.

Optimisation combinatoire, Combinatorial Pattern Matching, Triangle-Free 2-Matchings Revisited. String Processing and Information Retrieval, Sublinear Graph Approximation Algorithms. Property Testing, The Zero Exemplar Distance Problem.

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Comparative Genomics, On the Grundy Number of a Graph. Parameterized and Exact Computation, Journal of Combinatorial Optimization 18 :4, Theory of Computing Systems 45 :3, Algorithmica 55 :1, Journal of Lightwave Technology 27 , Machine Learning 76 :1, Discrete Applied Mathematics :9, Discrete Mathematics :6, Computing 84 , Wireless Communications and Mobile Computing 9 :3, Information Processing Letters :4, Discrete Mathematics :1, Object Association Across Multiple Cameras.

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Multi-Camera Networks, Bipartite Graph Matchings in the Semi-streaming Model. Colinear Coloring on Graphs. A General Testability Theory. Discrete Geometry for Computer Imagery, Journal of Discrete Algorithms 6 :4, European Journal of Operational Research :3, Journal of Graph Theory 59 :3, Journal of Combinatorial Optimization 16 :3, Biotechnology and Bioengineering :6, European Journal of Combinatorics 29 :6, Mathematical Programming :2, Expert Systems 25 :3, Wireless Communications and Mobile Computing 8 :5, PLoS Computational Biology 4 :5, e Journal of Combinatorial Theory, Series B 98 :3, Discrete Applied Mathematics :3, Computer Vision and Image Understanding :2, Parallel Computing 34 :1, Defect and Fault Tolerance.

Reconfigurable Computing, Stabilization, Safety, and Security of Distributed Systems, The Balanced Edge Cover Problem. Ad-hoc, Mobile and Wireless Networks, Journal of Applied and Industrial Mathematics 1 :4, Information Sciences , Performance Evaluation 64 , Frontiers of Computer Science in China 1 :4, Journal of Computational Biology 14 :7, Pattern Recognition Letters 28 :8, Journal of Algorithms 62 :2, Information Sciences :6, Journal of Combinatorial Optimization 13 :3, Telecommunication Systems 34 , David J.

Abraham , Robert W. Irving , Telikepalli Kavitha , and Kurt Mehlhorn. International Journal of Satellite Communications and Networking 25 :1, Constraints 11 :4, IEEE Globecom , Theoretical Computer Science :2, Journal of Global Optimization 36 :2, Acta Informatica 43 :3, Journal of Heuristics 12 , Naval Research Logistics 53 :6, European Journal of Combinatorics 27 :5, Bioinformatics 22 , Distributed Computing 18 :6, Operations Research Letters 34 :3, Pattern Recognition 39 :5, Journal of Computer Science and Technology 21 :3, Journal of Algorithms 59 :1, Theoretical Computer Science :3, Mathematical Programming , Global Constraints.

Handbook of Constraint Programming, Algorithms and Constraint Programming. Fractional Matching Via Balls-and-Bins. Expected-Case Analysis for Delayed Filtering. Recent Advances in Constraints, Matching Large Scale Ontology Effectively. Assignment Problems in Rental Markets.

Internet and Network Economics, Effective Large Scale Ontology Mapping. Knowledge Science, Engineering and Management, Quantum Algorithms for Matching and Network Flows. STACS , Academic Radiology 12 , Journal of Discrete Algorithms 3 , Journal of Combinatorial Optimization 9 :4, Constraints 10 :2, Network Algorithmics, Constraints 10 :1, On the Complexity of Several Haplotyping Problems.

Algorithms in Bioinformatics, Multiconsistency and Robustness with Global Constraints. Finding Graph Matchings in Data Streams. Approximation, Randomization and Combinatorial Optimization. What Would Edmonds Do? Typed Lambda Calculi and Applications, Pareto Optimality in House Allocation Problems.

Fast Algorithms for Weighted Bipartite Matching. Experimental and Efficient Algorithms, Mathematics of Operations Research 29 :4, Information Processing Letters 91 :6, Artificial Intelligence :1, Information Processing Letters 90 :5, Back Matter. Algorithmische Graphentheorie, International Conference on Parallel Processing, ICPP Journal of Algorithms 50 :1, Information Processing Letters 89 :2, Global Constraints and Filtering Algorithms. Constraint and Integer Programming, Looking at the Stars. Inner Rectangular Drawings of Plane Graphs.

Improved Algorithms for the Global Cardinality Constraint. Computer Networks 42 :4, Constrained Tree Inclusion. Evolutionary Algorithms and the Maximum Matching Problem. Alternating Paths along Orthogonal Segments. Semi-matchings for Bipartite Graphs and Load Balancing. Matching, Edge-Colouring, and Dimers.

Generic Programming, Computer Vision and Image Understanding 88 :3, Proceedings of the IEEE 90 :9, Journal of Scheduling 5 :3, Graph-Theoretical Methods in Computer Vision. Theoretical Aspects of Computer Science, Practical Aspects of Declarative Languages, Information and Computation :2, Acta Mathematicae Applicatae Sinica 17 :4, Biometrics 57 :2, Exact combinatorial algorithms: Ground states of disordered systems.

Phase Transitions and Critical Phenomena, On the fairness of scheduling algorithms for input-queued switches. Journal of the Operations Research Society of Japan 44 :2, European Transactions on Telecommunications 12 :1, Approximate Constrained Bipartite Edge Coloring.

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Tight Bounds on Maximal and Maximum Matchings. Parallel Computing 26 , Information Processing Letters 75 :4, Computer Networks 32 :3, Journal of the Operations Research Society of Japan 43 :1, Mining Structured Association Patterns from Databases. Knowledge Discovery and Data Mining. Current Issues and New Applications, Small Maximal Matchings in Random Graphs. Journal of Algorithms 33 :2, Japan Journal of Industrial and Applied Mathematics 16 :3, Networks 34 :1, Journal of Computational Physics :1, Naval Research Logistics 46 :1, Weimin Chen and Volker Turau. Esther M.

Mitchell , Steven S. Skiena , and Tae-Cheon Yang. A unifying framework for design and analysis of matching algorithms. Networks 33 :1, Linear Assignment Problems and Extensions. Handbook of Combinatorial Optimization, Edge Coloring of Bipartite Graphs with Constraints.

STACS 99, Journal of Parallel and Distributed Computing 55 :2, Journal of Algorithms 29 :2, Information Processing Letters 68 :3, Discrete Applied Mathematics 84 , Alexander Schrijver. Information Processing Letters 65 :1, A compiler for rewrite programs in associative-commutative theories.

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Principles of Declarative Programming, Randomization and Approximation Techniques in Computer Science, Qualitative Study of Geometric Constraints. Geometric Constraint Solving and Applications, Routing and Topology Embedding in Lightwave Networks. An Overview of Randomized Algorithms. Probabilistic Methods for Algorithmic Discrete Mathematics, Information Processing Letters 64 :3, Computing 59 :3, Algorithmica 18 :1, Algorithmica 17 :4, Rakesh M.

Systems and Computers in Japan 28 :3, Journal of Algorithms 22 :2, Experimental Mathematics 6 :1, Unstructured graph partitioning for sparse linear system solving. Solving Irregularly Structured Problems in Parallel, Two algorithms for three dimensional orthogonal graph drawing. Graph Drawing, All-cavity maximum matchings. On the equivalence in complexity among basic problems on bipartite and parity graphs. Algorithms for enumerating all perfect, maximum and maximal matchings in bipartite graphs. Sparse matrix ordering with Scotch.

High-Performance Computing and Networking, Knowledge-Centered Problem Solving Strategies. Intelligent Systems for Engineering, Mobile Multimedia Communications, On linear schedules of task graphs for generalized logp-machines. Euro-Par'97 Parallel Processing, Parallel Computing 22 , Discrete Applied Mathematics 71 , Discrete Applied Mathematics 69 :3, Discrete Applied Mathematics 68 , European Journal of Operational Research 91 :2, Parallel Computing 22 :4, Algorithmica 15 :6, Vineet Bafna and Pavel A.

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Combinatorics, Probability and Computing 5 :1, Algorithms — ESA '96, Algorithms for maximum matching and minimum fill-in on chordal bipartite graphs.