Approximation Algorithms for NP-hard Routing Problems
Author | : Greg Norman Frederickson |
Publisher | : |
Total Pages | : 184 |
Release | : 1977 |
Genre | : Algorithms |
ISBN | : |
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Author | : Greg Norman Frederickson |
Publisher | : |
Total Pages | : 184 |
Release | : 1977 |
Genre | : Algorithms |
ISBN | : |
Author | : Dorit S. Hochbaum |
Publisher | : Course Technology |
Total Pages | : 632 |
Release | : 1997 |
Genre | : Computers |
ISBN | : |
This is the first book to fully address the study of approximation algorithms as a tool for coping with intractable problems. With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms. APPROXIMATION ALGORITHMS FOR NP-HARD PROBLEMS is intended for computer scientists and operations researchers interested in specific algorithm implementations, as well as design tools for algorithms. Among the techniques discussed: the use of linear programming, primal-dual techniques in worst-case analysis, semidefinite programming, computational geometry techniques, randomized algorithms, average-case analysis, probabilistically checkable proofs and inapproximability, and the Markov Chain Monte Carlo method. The text includes a variety of pedagogical features: definitions, exercises, open problems, glossary of problems, index, and notes on how best to use the book.
Author | : Yuzhuang Hu |
Publisher | : |
Total Pages | : 296 |
Release | : 2009 |
Genre | : Approximation algorithms |
ISBN | : |
The Vehicle Routing Problem (VRP) is a generalization of the Traveling Salesman Problem (TSP) and is also one of the most challenging tasks in the area of combinatorial optimization. In the VRP we are given P vehicles and an undirected complete graph G = (V,E) where edge weights satisfying the triangle inequality. The objective is to find a separate tour for each vehicle while minimizing the total cost of the tours. In the Capacitated Vehicle Routing Problem (CVRP), each vehicle has a limited capacity K, and it is required that the vehicle should never exceed its capacity at any point of the tours. In this thesis we present approximation algorithms for the CVRP. The CVRP, in fact, represents a large class of TSP-like problems. We consider approximation algorithms for three variants of the CVRP, namely the Capacitated Vehicle Routing Problem with Pickups and Deliveries (CVRPPD), variants of the Cycle Covering Problem (CCP), and the Capacitated Vehicle Routing Problem with Multi-Depots. Many practical applications, such as mail delivery and bus routing, can be modeled by the CVRPPD. In this class of problems, we focus on the k-delivery Traveling Salesman Problem, the Capacitated Dial-a-Ride Problem, and the Black and White Traveling Salesman Problem (BWTSP). We propose a rule to improve the approximation ratios for the first two problems. We also give a constant factor matching based approximation algorithm for the BWTSP. In the second part of the thesis we investigate some NP-hard variants of the CCP. These variants consider two additional constraints. One constraint is on the number of vertices in each cycle, and the other is on the number of cycles appearing in a cycle cover. We present constant factor approximation algorithms for these problems. Different from the default settings of the CVRP, where only a central depot is involved, in the CVRP with Multi-Depots and Multi-Vehicles, the vehicles may start from different depots. In this category we study a model of the Multi-Depot Capacitated Vehicle Routing Problem (MDCVRP) and the Multi-Vehicle Scheduling Problem (MVSP). We propose a dynamic programming based method to design approximation algorithms for these problems.
Author | : Klaus Jansen |
Publisher | : Springer |
Total Pages | : 280 |
Release | : 2003-06-30 |
Genre | : Computers |
ISBN | : 3540457534 |
This book constitutes the refereed proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002, held in Rome, Italy in September 2002. The 20 revised full papers presented were carefully reviewed and selected from 54 submissions. Among the topics addressed are design and analysis of approximation algorithms, inapproximability results, online problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and applications to game theory and other fields.
Author | : Klaus Jansen |
Publisher | : Springer Science & Business Media |
Total Pages | : 280 |
Release | : 2002-09-02 |
Genre | : Business & Economics |
ISBN | : 3540441867 |
This book constitutes the refereed proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2002, held in Rome, Italy in September 2002. The 20 revised full papers presented were carefully reviewed and selected from 54 submissions. Among the topics addressed are design and analysis of approximation algorithms, inapproximability results, online problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and applications to game theory and other fields.
Author | : Klaus Jansen |
Publisher | : Springer |
Total Pages | : 290 |
Release | : 2003-07-31 |
Genre | : Computers |
ISBN | : 354044436X |
This book constitutes the refereed proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2000, held in Saarbrcken, Germany in September 2000. The 22 revised full papers presented together with four invited contributions were carefully reviewed and selected from 68 submissions. The topics dealt with include design and analysis of approximation algorithms, inapproximibility results, on-line problems, randomization techniques, average-case analysis, approximation classes, scheduling problems, routing and flow problems, coloring and partitioning, cuts and connectivity, packing and covering, geometric problems, network design, and various applications.
Author | : Klaus Jansen |
Publisher | : Springer Science & Business Media |
Total Pages | : 436 |
Release | : 2004-08-11 |
Genre | : Computers |
ISBN | : 3540228942 |
This book constitutes the joint refereed proceedings of the 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2004 and the 8th International Workshop on Randomization and Computation, RANDOM 2004, held in Cambridge, MA, USA in August 2004. The 37 revised full papers presented were carefully reviewed and selected from 87 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, approximation classes, online problems, graph algorithms, cuts, geometric computations, network design and routing, packing and covering, scheduling, game theory, design and analysis of randomised algorithms, randomized complexity theory, pseudorandomness, derandomization, probabilistic proof systems, error-correcting codes, and other applications of approximation and randomness.
Author | : Nitish Sabharwal |
Publisher | : LAP Lambert Academic Publishing |
Total Pages | : 56 |
Release | : 2012-06 |
Genre | : Computer algorithms |
ISBN | : 9783659150920 |
In this era of information technology, many decisions are made rapidly by computers in various industries to achieve some best possible goal or objective, from routing vehicles, to deciding inventory, model networks and for efficient data retrieval.For many such problems, we cannot conduct an exhaustive search of all the solutions to find the optimal solution in polynomial time, as they have an exponential population of possibilities. Such problems are referred to as NP-hard and we have focused on such type of problems in this monograph.We have proposed some interesting approximate algorithms and heuristics to solve the Traveling Salesman Problem and the Hamiltonian Cycle Problem and get good quality solutions.The computer simulations performed show the effectiveness of our algorithms.
Author | : Josep Diaz |
Publisher | : Springer Science & Business Media |
Total Pages | : 532 |
Release | : 2006-08-11 |
Genre | : Computers |
ISBN | : 3540380442 |
This is the joint refereed proceedings of the 9th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2006 and the 10th International Workshop on Randomization and Computation, RANDOM 2006. The book presents 44 carefully reviewed and revised full papers. Among the topics covered are design and analysis of approximation algorithms, hardness of approximation problems, small spaces and data streaming algorithms, embeddings and metric space methods, and more.