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gonzalez t handbook approximation algorithms metaheuristic 2007

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Textbook in PDF format Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical applications. It is the first book to comprehensively study both approximation algorithms and metaheuristics. Starting with basic approaches, the handbook presents the methodologies to design and analyze efficient approximation algorithms for a large class of problems, and to establish inapproximability results for another class of problems. It also discusses local search, neural networks, and metaheuristics, as well as multiobjective problems, sensitivity analysis, and stability. After laying this foundation, the book applies the methodologies to classical problems in combinatorial optimization, computational geometry, and graph problems. In addition, it explores large-scale and emerging applications in networks, bioinformatics, VLSI, game theory, and data analysis.Undoubtedly sparking further developments in the field, this handbook provides the essential techniques to apply approximation algorithms and metaheuristics to a wide range of problems in computer science, operations research, computer engineering, and economics. Armed with this information, researchers can design and analyze efficient algorithms to generate near-optimal solutions for a wide range of computational intractable problems. Basic Methodologies Approximation Algorithms Local Search, Artificial Neural Networks, and Metaheuristics Time and Space Complexity NP-Completeness Performance Evaluation of Algorithms Restriction Scheduling Partially Ordered Tasks Independent Tasks Relaxation: Linear Programming Approach Inapproximability Traditional Applications Computational Geometry and Graph Applications Large-Scale and Emerging Applications Steiner Trees Traveling Salesperson Tours Covering Points by Squares Rectangular Partitions Routing Multiterminal Nets Embedding Hyperedges in a Cycle Concluding Remarks Set Cover Shortest Superstring Problem K-Centers Connected Dominating Sets Minimum-Degree Spanning Trees Primal-Dual Methods Max Cut Unweighted Set Cover Lagrangian Relaxation for Fractional Set Cover Conclusions A Review of the Greedy Algorithm Directed Steiner Problems Layering Limiting the Number of Layers Description Density Bounding the Density of Augmenting Trees Approximation of k-DST Improving the Running Time Reducing the Maximum Degree The Modified Algorithm Height Reduction Rounding Randomized Rounding Metric Spaces Independent Rounding Simultaneous Rounding Extensions Filter and Round Iterated Rounding Pi Rounding Decompose and Round Complex Quadratic Optimization Discrete Problems Where Q Is Positive Semidefinite Continuous Problems Where Q Is Not Positive-Semidefinite Discrete Problems Where Q Is Not Positive-Semidefinite Extending Partial Small-Size Solutions Extending an Optimal Solution for a Single Subset Extend All Possible Solutions for Small Subsets Grouping Subsets of Elements Reducing the Number of Distinct Values in the Input Randomized Grouping Solving LP for a Subset of Elements LP Rounding Combined with Enumeration A Scheme for CIP… Approximation Schemes for Geometric Problems Randomized Dissection Shifted Plane Partitions Rounding Interval Partitioning Separation Notation Extended Bellman–Ford Algorithm Rounding Interval Partitioning and Separation Hybrid Interval Partitioning Heuristics (HIPHs) Summary of Algorithms and Techniques Asymptotic Polynomial-Time Approximation Scheme Restricted Bin Packing Linear Grouping Asymptotic Fully Polynomial-Time Approximation Scheme Fractional Bin Packing and Rounding AFPTAS for Bin Packing Related Results Problem SET COVER A Randomized Rounding Approximation to Set Cover Approximate Counting Using the Markov Chain Monte Carlo Method Radiocolorings of Graphs Outline of Our Approach Rapid Mixing An FPRAS for Radiocolorings with lambda Colors Small Dominating Sets Greedy Greedy Hordes Small Connected Dominating Sets Coloring: The Extraordinary Career of a Trivial Algorithm Coloring with Martingales Matchings Distributed Maximal Independent Set LP-Based Distributed Algorithms What Can and Cannot Be Computed Locally? A Case Study: Minimum Spanning Tree Analysis on Single Instances Comparative Analysis on Single Instances Comparative Analysis on Instance Ensembles Optimisation Algorithms Analysis on Single Instances Analysis on Instance Ensembles Impact of Parameter Settings Stagnation Detection Functional Characterisation of Empirical RTDs Extensions Basic Definitions The Linear Reducibility Strict Reducibility and Complete Problems in NPO AP-Reducibility APX-Completeness Negative Results Based on APX-Completeness FT-Reducibility Gadgets, Reductions, and Inapproximability Results Toward a New Measure of Approximation Paradigm Min Hereditary Cover Min Coloring Bin Packing Traveling Salesman Problems Asymptotic Differential Approximation Ratio The Class -DAPX DAPX- and Poly-DAPX-Completeness Poly-DAPX-Completeness Discussion and Final Remarks Inapproximability The Emergence of the PCP Theory Gap Problems, Karp Reductions, and the PCP Theorem Karp reduction from languages to gap problems Probabilistic Oracle Machines (POM) FGLSS (Feige–Goldwasser–Lovasz–´Safra–Szegedy) transformation Codes and PCPs The Long Code Holographic Proofs and the Proof Recursion Idea Reducing the Query Size Composed Verifier Reducing the Alphabet Size Powering Local Search, Neural Networks, and Metaheuristics Algorithm IterativeImprovement (S, N, c) The Complexity of Computing Local Optimum Solutions Local Search in Approximation Algorithms An Approximation Algorithm for Multiprocessor Scheduling Finding Spanning Trees with Many Leaves Local Search Algorithm for the k-Median Problem Iterative Improvement Simulated Annealing Dynamic Local Search Iterated Local Search Population-Based SLS Methods Evolutionary Algorithms Discussion and Research Directions Partitioning Problems and Multiexchange Neighborhoods Local Augmentation Algorithm for N(S) Path Exchange as a Cyclic Exchange Extended Neighborhoods and Domination Analysis Approximate Local Search Algorithm Epsilon-local search Introduction: The Role of the User in Heuristics Asymptotic Results Are Irrelevant for Optimization Prohibition-Based Diversification: Tabu Search The Escape Mechanism Fast Algorithms for Using the Search History Hashing Combined with Persistent Red-Black Trees Applications of Reactive Search and the Maximum Clique Example Reactive Local Search for Max Clique Choice of the Best Neighbor Reaction and Periodic Restart Related Reactive Approaches Feedforward Neural Networks Approximation Properties Learning Theoretic Results VC-Dimension Approach Network Definition and Performance Measure Unrolling a Network Derivation of BPTT Formulation Real-Time Backpropagation through Time Computational Capabilities of Discrete and Continuous Recurrent Networks Memory Structures Search Strategies Advanced Designs: Strategic Oscillation and Path Relinking The Linear-Ordering Problem The Tabu Cycle and Conditional Probability Methods Evolutionary Algorithms Reproduction Operators Exploitation versus Exploration Families of Evolutionary Algorithms Constrained Problems Multiobjective Problems EAs in the Context of Metaheuristics Basic Simulated Annealing Dynamic Cooling Schedules Asymptotic Convergence Equilibrium Statistics From Biology to Algorithms Ants Algorithms The Ant Colony Optimization Metaheuristic UpdatePheromones Example: The Traveling Salesman Problem Ant System MAX-MIN Ant System Ant Colony System Parallel ACO Implementations Dissecting a Basic Memetic Algorithm Conclusions and Future Directions Multiobjective Optimization, Sensitivity Analysis, and Stability Min Max Optimality NP-Completeness Intractability A Biobjective Scheduling Problem The Bicriteria Shortest Path Problem on Acyclic Graphs The Bicriteria MAX-CUT Problem Pareto Set Approach An Approximate Pareto Set with a Budget Approach The Bicriteria TSP (, ) Basics Component-Wise Acceptance Criterion Extensions of Tabu Search Indirect Use of the Component-Wise Ordering Scalarized Acceptance Criterion Proprietary Simulated Annealing Sequential Combination Iterative Combination Conclusions Preliminaries Issues in Sensitivity Analysis Parametric Search Combinatorial Complexity Bounds for Small-Dimensional Problems Linear Programming Shortest Paths and Related Problems Sensitivity Analysis of NP-Hard Problems Graphs of Bounded Tree Width kappa Best Solutions and Sensitivity Analysis Definition of the Stability of Approximation Algorithms Stable Approximation Algorithms for the TSP Lower Bounds and the Situation Inside Delta-TSP Discussion and Related Work Traditional Applications Online Algorithms Bounded-Space Online Algorithms Better Online Algorithms Lower Bounds for Online Algorithms Offline Algorithms Special Case Optimality Linear-Time Algorithms Absolute Worst-Case Ratios Parallel Algorithms Maximizing the Number of Items Packed Bounds on the Number of Items per Bin Dynamic Bin Packing Fragmentable Bin Packing Packing Nodes of Graphs Changing the Bin Size Variable-Sized Bin Packing Bin Covering Next Fit Decreasing Height Online Results Offline Results Two-Dimensional Bin Packing Offline Results Online and Offline Results Three- and More Dimensional Bin Packing Vector Packing Items Appear from the Top Packing Rectangles in a Single Rectangle Rectangle Packing Problem Coding Schemes for Rectangle Packing Heuristics for Rectangle Packing Metaheuristics for Rectangle Packing Irregular Packing Problem Job Interval Stabbing Problem (JIS) Previous Research The Local Covering Algorithm for the Weighted Set Packing Problem Algorithm ALG The Case of Unit Demands: Algorithm ALG Requirement Additional Definitions Results for Metric Instances Results for Geometric Versions Results for Metric Instances Results for Nonmetric Instances Results for Other Dispersion Problems Requirement Results for Maximizing Internode Distance Results for Geometric Versions Future Directions Dual-Fitting and Factor-Revealing LP The -Approximation Algorithm The -Approximation Algorithm Quasi-Greedy Algorithm for Two-Level Facility Location The Primal-Dual Algorithm of Goemans and Williamson History of the Results A -Approximation Algorithm for kappa-Minimum Spanning Tree and kappa-Traveling Salesman Problem History of the Results Minimum Latency Problem A -Approximation Algorithm for the Minimum Latency Problem Related Work Tolerating Faulty Hosts Performance Considerations The JICOS Branch-and-Bound Framework The Measurements Minimax Theorem The Steiner Ratio in Banach Spaces Zelikovsky’s Idea Variable Metric Method Approximation for Geometric Steiner Minimum Trees Guillotine Cut m-Guillotine Subdivision Portals Comparison and Combination The Greedy Triple Contraction and Batched Greedy Algorithms Generation of Triples Computing Maximum Cost Edge on a Tree Path Experimental Results Boolean Function Feasible (TS) Algorithm Largest-Optional-Processing-Time-First Algorithm Smallest-Optional-Processing-Time-First Proofs of Assertions Conclusions A /-Approximation Algorithm for IMT Scheduling An AFPTAS for IMT Scheduling An Approximation Algorithm for PCMT Scheduling with Tree Precedence Approximation Algorithms for PCMT Scheduling Improved Approximation Algorithm for PCMT Scheduling Approximation Algorithm for PCMT Scheduling (MT) Vehicle Scheduling Problem In Trees In Paths Multi-Vehicle Scheduling Classical Planning Methods for Solving Classical Planning Problems Relaxations of Classical Planning Problems Heuristic Guidance Using Relaxed Planning Problems Solution Approximations Using Relaxation Heuristic Guidance via Subproblem Identification Local Search Neighborhoods for Planning Selecting the Successor Related Problems and Complexity Local Search Lagrangian Relaxation Lagrangian Heuristics Metaheuristics EC Probe Algorithms TSEC and PREC Branch-and-Bound Algorithms Computational Results Performance Guarantee Iteration (step j ) Performance Bound for Maxsat Problem Performance Bound for Minsat Problem Part V: Computational Geometry and Graph Applications Properties of D Triangulations Some Triangulation Heuristics for Convex Polyhedra D Minimum Weight Triangulation An O(log n) Approximation Algorithm for Point Sets A Constant Factor Approximation Algorithm for Point Sets D Maximum Weight Triangulation Improving the Approximation Ratio to A Better Approximation Algorithm Lower Bound for Approximation Ratio Special Cases Multiconnectivity Problems Overview of the Results Preliminaries First Approach: Polynomial-Time Pseudo-Approximation Schemes m-Portal-Respecting Graphs Dynamic Programming and Finding an Optimal m-Portal-Respecting r-Light Solution Patching Lemma: Reducing Number of Crossings Using Steiner Points Structure Theorem: There Is Always a Good r-Light Steiner k-VCSS Sketch of the proof PTAS for Geometric Multiconnectivity Problems Local Decomposition Lemma Filtering Lemma Concluding: Structure Theorem for kappa-Vertex Connectivity Faster PTAS for Euclidean kappa-ECSSM and -Connected Graphs -Connected Graphs Are Not Worse than -Connected Multigraphs Lower Bounds Steiner kappa-Connectivity—Real Approximation Schemes Finding Low-Cost kappa-VCSS and kappa-ECSS in Planar Graphs Constructing t-Spanners Skip-List Spanners The Well-Separated Pair Decomposition-Graph The Greedy-Graph Approximating the Dilation Structural Properties Algorithmic Questions Low Detour Embeddings of Point Sets Exclusion and Inclusion Regions Stars Well-Separated Pairs The Split Tree Exact Algorithms for Proximity Problems The kappa Closest Pairs Problem The All-Nearest Neighbors Problem The Spanner Problem The Minimum Spanning Tree Problem The kappath Closest Pair Problem Generalization to Metric Spaces A Divide-and-Conquer Algorithm Approximation Bound Improved Approximation Bound Concluding Remarks Definitions and Notation Planar Digital Objects A General Coding Scheme Encoding by Least Squares Fit Polynomials Encoding Planar Regions Threshold Functions on Binary Inputs Concluding Remarks Analysis of the MST Algorithm Triangular Structures and Better Approximations Analysis of the Triangular Structure Algorithms Outerplanar Subgraphs Practical Results and Discussion Complexity of Disjoint-Path Problems Main Threads Greedy Algorithms Randomized Rounding and UFP Packing Integer Programs and UFP Combinatorial Algorithms and Other Results Variants of the Basic Problems Generalized Steiner Network Small Requirements Preliminaries Edge-Covers of Set-Functions and LP-Relaxations Connectivity Augmentation Augmenting a kappa-Connected Graph to Be (kappa + )-Connected Algorithm Based on Edge-Covers LP-Rounding Algorithm for Directed Min-Size kappa-ECSS Undirected Graphs A -Approximation Algorithm for Undirected Edge-GSN Approximation Algorithm for kappa-CSS Hardness of Approximation: Three Typical Reductions Minimum Routing Cost Spanning Tree Routing Loads, Separators, and General Stars A Reduction to the Metric Case Approximation Ratio Finding the Optimal kappa-Star Product-Requirement Communication Spanning Tree A Polynomial-Time Approximation Scheme Sum-Requirement Communication Spanning Tree Multiple Sources MRCT Approximating the -MRCT The Weighted -MRCT On Metric Graphs The p-OCT Concluding Remarks Bounds on the Bisection Width Global Heuristics The Multilevel Scheme Approximation Algorithms for Cardinality Matching /-Approximation Algorithms for Maximum-Weighted Matching / – epsilon Approximation Algorithms for Maximum-Weighted Matching The Kernighan–Lin Refinement Heuristic The Helpful-Set Refinement Heuristic Graph Partitioning Tools Discussion Integrated Circuit Design Definitions and Terminology Summary of Techniques and Their Scale Dependence Branch and Bound Other Types of Algorithms The Fiduccia–Mattheyses Heuristic Gain Computation and Gain Update Custom Data Structures Multilevel Fiduccia–Mattheyses Partitioning Framework Coarsening Refinement hMETIS Benchmark Format Appendix: Empirical Results Deterministic Algorithms Sequential Algorithm Randomized Optimal Solution Randomized Approximate Solution Sequential Algorithm CREW Implementation MVE with Respect to APSPs Sequential Algorithm CRCW Implementation Benchmark Instances Preprocessing and Heuristic Reduction Rules Construction Heuristics Strategy : kappa Fixed, Complete Colorings Strategy : kappa Variable, Complete Colorings Neighbourhood Examination and Data Structures Strategy : kappa Fixed, Complete Colorings Experimental Comparison of Stochastic Local Search Algorithms A Greedy Approach An Example where SGA and the Multistart Greedy Algorithm Fail An Ant Colony Optimization Approach Algorithmic Framework Solution Construction Escape Mechanism Experiments Problem Instances Experiments and Results Part VI: Large-Scale and Emerging Applications Multicast Routing in Ad Hoc Networks Problem Formulation NP-Completeness Greedy-Based Heuristic Algorithm Distributed Variant Performance Analysis The Cost over Progress Framework Geographic Multicasting with Cost over Progress Greedy Selection of Set Partitions Motivation Technicalities Our Tree-Based Clustering Algorithm The Tree-Based Cluster Split Algorithm: Single-Link Failure The Tree-Based Cluster Split Algorithm: Single-Node Failure Merging Clusters Performance Metrics Simulation Results Application Concluding Remarks Notation for Topology Control Problems A General Framework An Approximation Algorithm for (UNDIR, -NODE-CONNECTED, TOTALP) Proof of Lemma An Approximation Algorithm for (UNDIR, -EDGE-CONNECTED, TOTALP) Improvement by Calinescu and Wan Minimum Cost Tree with a Diameter Constraint Distributed Approximation Algorithms Distributed Algorithms for (GEOMETRIC, -NODE-CONNECTED, TOTALP) Proof of Theorem A Summary of Results for Other Topology Control Problems Geometrical Spanner Efficient Localized Construction Relative Neighborhood Graph Local Delaunay Graph Bounded-Degree Spanner and Yao’s Family Sparsified Yao Ordered Yao Delaunay Triangulation Plus Yao Structure Local Delaunay Graph Plus Yao Structure Gabriel Graph Plus Yao Structure Other Spanners Mathematical Models of Multicast Network Existing Approach for Siblings Classification Hamming Distance Classification Approach Binary Hamming Distance Classification Algorithm Analysis on Inference Accuracy of Hamming Distance Classification Approach Experimental Results for Topology Inference Hamming Distance Matrix for Internal Loss/Delay Performance Analysis Topology Inference for General Trees The Undirected MCHEC Problem The Re-Embedding Algorithm The Clockwise (/)-Rounding Algorithm The Randomized Rounding Algorithm The Directed MCHEC Problem Centralized Approximation Algorithms The Charikar–Naor–Schieber Algorithms Beta-Convex Steiner Tree Approximation Algorithms Beta-Convex Approximation for QoSMT with Two Rates Beta-Convex Approximation for QoSMT with Unbounded Number of Rates A Simple Integer Linear Program (ILP) Formulation Two Primal-Dual Methods for the Simple ILP Formulation Primal-Dual -Approximation Algorithm Experimental Study The Hierarchical Decomposition Technique The Prefix Technique Supervised Overlay Networks Putting the Pieces Together Maintaining Condition Maintaining a Dynamic Hypercube Maintaining a Dynamic deBruijn Graph Overlay Networks Based on Prefix Connections The PRR Scheme Prefix Routing Route, Join, and Leave The LAND Scheme Other Related Work Problem Formulation Uniform Lengths The Dichotomic Algorithm Two Channels Nonuniform Lengths The Greedy Algorithm The Dlinear Algorithm Experimental Tests Conclusions Fixed-Parameter Tractability A Biclique-Oriented Approach Reduction Rules for the (alpha, beta) - kappa-Feature Set Problem A Hamiltonian Path-Motivated Approach for Gene Ordering Computational Experiments and Results Background Information Polymerase Chain Reaction Terminology NP-Completeness of Primer Selection Problem and Degenerate Primer Selection Problem Algorithms for PSP Algorithm HYDEN Algorithm DePiCt Algorithm Multiple Iterative Primer Selector Algorithm Degenerate Primer Search (DPS) The Planted Motif Search Problem Algorithm PMS The Closest String Problem An Approximate Solution Using Integer Programming A ( + epsilon) Polynomial-Approximate Scheme Simple Approximation Schemes A ( + epsilon) Polynomial-Approximation Scheme Framework for Pairwise Sequence Comparison Fractional Programming ANLA Algorithms Approximation Algorithms for Partial Constraint Satisfaction Normalized Local Alignment Discussion Single Nucleotide Polymorphisms and Haplotypes Haplotype Blocks and Tag SNPs The Problem of Missing Data Finding Robust Tag SNPs Problem: Minimum Robust Tag SNPs The First Greedy Algorithm The Second Greedy Algorithm The Iterative LP-Relaxation Algorithm Problem: Minimum Auxiliary Tag SNPs Results on Simulated Data Results on Biological Data Discussion Preliminaries -D Lattice Packing with Translation -D Lattice Packing with Translation and Rotation Shaking a Lattice Packing Trimming and Packing Extensions to Three or Higher Dimensions Experimental Studies Background Mathematical Formulation Iterative Improvement over Feasible Placements Iterative Improvement over Infeasible Placements Cutsize Minimization Partitions Guided by Analytical Placements Multiscale Methods Coarsening Example: APlace Comparison to APlace Timing Problem Formulation Integrated Global Routing and Bounded Wireload Buffer Insertion Problem Gadget Graph and Integer Program Formulation The Approximation Algorithm Area and Congestion Trade-Off Curve Handling Multipin Nets Polarity Constraints Delay Constraints Experimental Results Conclusions Selfish Tasks: The KP and CKN Models Price of Anarchy for the KP Model Coordination Mechanisms for the CKN Model Approximate Stability for the CKN Model Truthful Algorithms Truthful Algorithm for Scheduling Selfish Tasks Monotonicity A Truthful Algorithm for the AT Model Pure Equilibria Coordination Mechanisms Results for the AT Model Models and Definitions A Convex Formulation for a Class of General Equilibrium Model Homogeneous Utility Functions Ellipsoid Algorithm Approximation Algorithm for Indivisible Goods Hardness Results Approximation Algorithms Algorithm Mechanism Design Binary Demand Games and General Demand Games Untruthfulness of VCG Mechanism: An Example Untruthfulness of VCG Mechanism: General Results Characterize the Strategyproof Mechanism Simple Composition Technique Complex Composition Technique Characterize the Strategyproof Mechanism DiffServ Multicast Game Literature Review Definitions and Problems The Vopt or the … Measure Beyond … Error: Workloads, Piecewise Polynomials … and Variants A Compact Primer on Compact Wavelets Wavelet Synopses and … Theory Streaming PTAS for Haar Systems Restricted Optimizations From (Haar) Wavelets Form Histograms Notes Applications of Reputation Management Motivating Cooperation Design Requirements for a Reputation System Direct versus Indirect Evidence Second-Order Reputation Motivation Is Not a Problem: Dissenting Views Other Design Issues Complaints-Based Trust EigenTrust ROCQ Conclusions and Future Work Color Spaces for Quantization Image-Independent Quantization Image-Dependent, Context-Free Quantization Feedback-Based Quantization

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gonzalez t handbook approximation algorithms metaheuristic 2007

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