Combinatorial algorithms : generation, enumeration, and search [electronic resource] / Donald L. Kreher, Douglas R. Stinson.

By: Kreher, Donald L [author.]Contributor(s): Stinson, Douglas R. (Douglas Robert), 1956- [author.]Material type: TextTextLanguage: English Series: Publisher: Boca Raton : CRC Press, 2020Edition: 1stDescription: 1 online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781000141375; 1000141373; 9781003068006; 1003068006; 9781000120042; 100012004X; 9781000102871; 1000102874Subject(s): Combinatorial analysis | Algorithms | MATHEMATICS / General | MATHEMATICS / Number Theory | MATHEMATICS / CombinatoricsDDC classification: 511.6 LOC classification: QA164Online resources: Taylor & Francis Click here to view. | OCLC metadata license agreement Summary: This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as:CombinationsPermutationsGraphsDesignsMany classical areas are covered as well as new research topics not included in most existing texts, such as:Group algorithmsGraph isomorphismHill-climbingHeuristic search algorithmsThis work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.
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Previously issued in print: 1999.

Structures and Algorithms<BR>What are Combinatorial Algorithms?<BR>What are Combinatorial Structures?<BR>What are Combinatorial Problems?<BR>O-Notation<BR>Analysis of Algorithms<BR>Complexity Classes<BR>Data Structures<BR>Algorithm Design Techniques<BR>Generating Elementary Combinatorial Objects<BR>Combinatorial Generation<BR>Subsets<BR>k-Element Subsets<BR>Permutations<BR>More Topics in Combinatorial Generation<BR>Integer Partitions<BR>Set Partitions, Bell and Stirling Numbers<BR>Labeled Trees<BR>Catalan Families<BR>Backtracking Algorithms<BR>Introduction<BR>A General Backtrack Algorithm<BR>Generating All Cliques<BR>Estimating the Size of a Backtrack Tree<BR>Exact Cover<BR>Bounding Functions<BR>Branch-and-Bound<BR>Heuristic Search<BR>Introduction to Heuristic Algorithms<BR>Design Strategies for Heuristic Algorithms<BR>A Steepest-Ascent Algorithm for Uniform Graph Partition<BR>A Hill-Climbing Algorithm for Steiner Triple Systems<BR>Two Heuristic Algorithms for the Knapsack Problem<BR>A Genetic Algorithm for the Traveling Salesman Problem<BR>Groups and Symmetry<BR>Groups<BR>Permutation Groups<BR>Orbits of Subsets<BR>Coset Representatives<BR>Orbits of k-tuples<BR>Generating Objects Having Automorphisms<BR>Computing Isomorphism<BR>Introduction<BR>Invariants<BR>Computing Certificates<BR>Isomorphism of Other Structures<BR>Basis Reduction<BR>Introduction<BR>Theoretical Development<BR>A Reduced Basis Algorithm<BR>Solving Systems of Integer Equations<BR>The Merkle-Hellman Knapsack System<BR>Bibliography<BR>Algorithm Index<BR>Problem Index<BR>Index.

This textbook thoroughly outlines combinatorial algorithms for generation, enumeration, and search. Topics include backtracking and heuristic search methods applied to various combinatorial structures, such as:CombinationsPermutationsGraphsDesignsMany classical areas are covered as well as new research topics not included in most existing texts, such as:Group algorithmsGraph isomorphismHill-climbingHeuristic search algorithmsThis work serves as an exceptional textbook for a modern course in combinatorial algorithms, providing a unified and focused collection of recent topics of interest in the area. The authors, synthesizing material that can only be found scattered through many different sources, introduce the most important combinatorial algorithmic techniques - thus creating an accessible, comprehensive text that students of mathematics, electrical engineering, and computer science can understand without needing a prior course on combinatorics.

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