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BL
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| Record Number
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662356
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| Doc. No
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dltt
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| Main Entry
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Garg, Vijay K., (Vijay Kumar),1963-
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| Title & Author
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Introduction to lattice theory with computer science applications /\ Vijay K. Garg
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| Page. NO
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1 online resource
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| ISBN
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9781119069713
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: 1119069718
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9781119069737
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1119069734
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9781118914373 (cloth)
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9781119069706
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111906970X
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1118914376
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| Bibliographies/Indexes
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Includes bibliographical references and index
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| Contents
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Introduction -- Introduction -- Relations -- Partial Orders -- Join and Meet Operations -- Operations on Posets -- Ideals and Filters -- Special Elements in Posets -- Irreducible Elements -- Dissector Elements -- Applications: Distributed Computations -- Applications: Combinatorics -- Notation and Proof Format -- Problems -- Bibliographic Remarks -- Representing Posets -- Introduction -- Labeling Elements of The Poset -- Adjacency List Representation -- Vector Clock Representation -- Matrix Representation -- Dimension-Based Representation -- Algorithms to Compute Irreducibles -- Infinite Posets -- Problems -- Bibliographic Remarks -- Dilworth's Theorem -- Introduction -- Dilworth's Theorem -- Appreciation of Dilworth's Theorem -- Dual of Dilworth's Theorem -- Generalizations of Dilworth's Theorem -- Algorithmic Perspective of Dilworth's Theorem -- Application: Hall's Marriage Theorem -- Application: Bipartite Matching -- Online Decomposition of Posets -- A Lower Bound on Online Chain Partition -- Problems -- Bibliographic Remarks -- Merging Algorithms -- Introduction -- Algorithm to Merge Chains in Vector Clock Representation -- An Upper Bound for Detecting an Aniichain of Size K -- A Lower Bound for Detecting an Antichain of Size K -- An Incremental Algorithm for Optimal Chain Decomposition -- Problems -- Bibliographic Remarks -- Lattices -- Introduction -- Sublattices -- Lattices as Algebraic Structures -- Bounding The Size of The Cover Relation of a Lattice -- Join-Irreducible Elements Revisited -- Problems -- Bibliographic Remarks -- Lattice Completion -- Introduction -- Complete Lattices -- Closure Operators -- Topped n-Structures -- Dedekind-Macneille Completion -- Structure of Dedekind-Macneille Completion of a Poset -- An Incremental Algorithm for Lattice Completion -- Breadth First Search Enumeration of Normal Cuts -- Depth First Search Enumeration of Normal Cuts -- Application: Finding the Meet and Join of Events -- Application: Detecting Global Predicates in Distributed Systems -- Application: Data Mining -- Problems -- Bibliographic Remarks -- Morphisms -- Introduction -- Lattice Homomorphism -- Lattice Isomorphism -- Lattice Congruences -- Quotient Lattice -- Lattice Homomorphism and Congruence -- Properties of Lattice Congruence Blocks -- Application: Model Checking on Reduced Lattices -- Problems -- Bibliographic Remarks -- Modular Lattices -- Introduction -- Modular Lattice -- Characterization of Modular Lattices -- Problems -- Bibliographic Remarks -- Distributive Lattices -- Introduction -- Forbidden Sublattices -- Join-Prime Elements -- Birkhoff's Representation Theorem -- Finitary Distributive Lattices -- Problems -- Bibliographic Remarks -- Slicing -- Introduction -- Representing Finite Distributive Lattices -- Predicates on Ideals -- Application: Slicing Distributed Computations -- Problems -- Bibliographic Remarks -- Applications of Slicing to Combinatorics -- Introduction -- Counting Ideals -- Boolean Algebra and Set Families -- Set Families of Size k -- Integer Partitions -- Permutations -- Problems -- Bibliographic Remarks -- Interval Orders -- Introduction -- Weak Order -- Semiorder -- Interval Order -- Problems -- Bibliographic Remarks -- Tractable Posets -- Introduction -- Series-Parallel Posets -- Two-Dimensional Posets -- Counting Ideals of a Two-Dimensional Poset -- Problems -- Bibliographic Remarks -- Enumeration Algorithms -- Introduction -- BFS Traversal -- DFS Traversal -- LEX Traversal -- Uniflow Partition of Posets -- Enumerating Tuples of Product Spaces -- Enumerating All Subsets -- Enumerating All Subsets of Size k -- Enumerating Young's Lattice -- Enumerating Permutations -- Lexical Enumeration of All Order Ideals of a Given Rank -- Problems -- Bibliographic Remarks -- Lattice of Maximal Antichains -- Introduction -- Maximal Antichain Lattice -- An Incremental Algorithm Based on Union Closure -- An Incremental Algorithm Based on BFS -- Traversal of the Lattice of Maximal Antichains -- Application: Detecting Antichain-Consistent Predicates -- Construction and Enumeration of Width Antichain Lattice -- Lexical Enumeration of Closed Sets -- Construction of Lattices Based on Union Closure -- Problems -- Bibliographic Remarks -- Dimension Theory -- Introduction -- Chain Realizers -- Standard Examples of Dimension Theory -- Relationship Between the Dimension and the Width of a Poset -- Removal Theorems for Dimension -- Critical Pairs in the Poset -- Rectangle Realizers -- Order Decomposition Method and Its Applications -- Problems -- Bibliographic Remarks -- Fixed Point Theory -- Complete Partial Orders -- Knaster-Tarski Theorem -- Application: Defining Recursion Using Fixed Points -- Problems -- Bibliographic Remarks
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| Subject
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Computer science-- Mathematics.
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| Subject
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Engineering mathematics.
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| Subject
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Lattice theory.
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| Dewey Classification
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004.01/51
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| LC Classification
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QA76.9.L38
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| Added Entry
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Ohio Library and Information Network.
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