Approximation Algorithms

Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians.

[1]  H. Kuhn The Hungarian method for the assignment problem , 1955 .

[2]  T. C. Hu,et al.  Multi-Terminal Network Flows , 1961 .

[3]  Ronald L. Graham,et al.  Bounds for certain multiprocessing anomalies , 1966 .

[4]  Ronald L. Graham,et al.  Bounds on Multiprocessing Timing Anomalies , 1969, SIAM Journal of Applied Mathematics.

[5]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[6]  László Lovász,et al.  On the ratio of optimal integral and fractional covers , 1975, Discret. Math..

[7]  Oscar H. Ibarra,et al.  Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems , 1975, JACM.

[8]  Leslie E. Trotter,et al.  Vertex packings: Structural properties and algorithms , 1975, Math. Program..

[9]  Teofilo F. Gonzalez,et al.  P-Complete Approximation Problems , 1976, J. ACM.

[10]  Ellis Horowitz,et al.  Exact and Approximate Algorithms for Scheduling Nonidentical Processors , 1976, JACM.

[11]  L. Lovász Combinatorial problems and exercises , 1979 .

[12]  George L. Nemhauser,et al.  Easy and hard bottleneck location problems , 1979, Discret. Appl. Math..

[13]  Leslie G. Valiant,et al.  The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..

[14]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[15]  J. Plesník A bound for the Steiner tree problem in graphs , 1981 .

[16]  H. Wolkowicz,et al.  Some applications of optimization in matrix theory , 1981 .

[17]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[18]  Richard M. Karp,et al.  An efficient approximation scheme for the one-dimensional bin-packing problem , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[19]  Richard M. Karp,et al.  Monte-Carlo algorithms for enumeration and reliability problems , 1983, 24th Annual Symposium on Foundations of Computer Science (sfcs 1983).

[20]  Teofilo F. GONZALEZ,et al.  Clustering to Minimize the Maximum Intercluster Distance , 1985, Theor. Comput. Sci..

[21]  David B. Shmoys,et al.  Using dual approximation algorithms for scheduling problems: Theoretical and practical results , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[22]  Mark W. Krentel The Complexity of Optimization Problems , 1986, Computational Complexity Conference.

[23]  P. Raghavan Probabilistic construction of deterministic algorithms: Approximating packing integer programs , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[24]  David B. Shmoys,et al.  A unified approach to approximation algorithms for bottleneck problems , 1986, JACM.

[25]  Agostino Villa,et al.  Network decomposition for the optimization of connection structures , 1986, Networks.

[26]  Leslie G. Valiant,et al.  Random Generation of Combinatorial Structures from a Uniform Distribution , 1986, Theor. Comput. Sci..

[27]  C. P. Schnorr,et al.  A Hierarchy of Polynomial Time Lattice Basis Reduction Algorithms , 1987, Theor. Comput. Sci..

[28]  R. Kannan ALGORITHMIC GEOMETRY OF NUMBERS , 1987 .

[29]  Ravi Kannan,et al.  Minkowski's Convex Body Theorem and Integer Programming , 1987, Math. Oper. Res..

[30]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988 .

[31]  M. Overton On minimizing the maximum eigenvalue of a symmetric matrix , 1988 .

[32]  Milena Mihail,et al.  On Coupling and the Approximation of the Permanent , 1989, Inf. Process. Lett..

[33]  Robert W. Irving,et al.  The Stable marriage problem - structure and algorithms , 1989, Foundations of computing series.

[34]  Richard M. Karp,et al.  Monte-Carlo Approximation Algorithms for Enumeration Problems , 1989, J. Algorithms.

[35]  David P. Williamson,et al.  Analyzing the Held-Karp TSP Bound: A Monotonicity Property with Application , 1990, Inf. Process. Lett..

[36]  Samir Khuller,et al.  Planar Graph Coloring is not Self-Reducible, Assuming P != NP , 1991, Theor. Comput. Sci..

[37]  L. Khachiyan,et al.  On the conductance of order Markov chains , 1991 .

[38]  Mihalis Yannakakis,et al.  On the approximation of maximum satisfiability , 1992, SODA '92.

[39]  Samir Khuller,et al.  Biconnectivity approximations and graph carvings , 1992, STOC '92.

[40]  Alistair Sinclair,et al.  Algorithms for Random Generation and Counting: A Markov Chain Approach , 1993, Progress in Theoretical Computer Science.

[41]  Paul D. Seymour,et al.  Packing directed circuits fractionally , 1995, Comb..

[42]  Satish Rao,et al.  An approximate max-flow min-cut relation for undirected multicommodity flow, with applications , 1995, Comb..

[43]  David R. Karger,et al.  A randomized fully polynomial time approximation scheme for the all terminal network reliability problem , 1995, STOC '95.

[44]  Samir Khuller,et al.  Improved approximation algorithms for uniform connectivity problems , 1995, STOC '95.

[45]  Nathan Linial,et al.  The geometry of graphs and some of its algorithmic applications , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[46]  Ramesh Hariharan,et al.  Derandomizing semidefinite programming based approximation algorithms , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[47]  Mark Jerrum,et al.  A Very Simple Algorithm for Estimating the Number of k-Colorings of a Low-Degree Graph , 1995, Random Struct. Algorithms.

[48]  Claus-Peter Schnorr,et al.  The Generalized Gauss Reduction Algorithm , 1996, J. Algorithms.

[49]  Howard J. Karloff,et al.  How good is the Goemans-Williamson MAX CUT algorithm? , 1996, STOC '96.

[50]  Joseph S. B. Mitchell,et al.  Guillotine subdivisions approximate polygonal subdivisions: a simple new method for the geometric k-MST problem , 1996, SODA '96.

[51]  Prasad Tetali,et al.  On the mixing time of the triangulation walk and other Catalan structures , 1997, Randomization Methods in Algorithm Design.

[52]  Uri Zwick,et al.  A 7/8-approximation algorithm for MAX 3SAT? , 1997, Proceedings 38th Annual Symposium on Foundations of Computer Science.

[53]  Samir Khuller,et al.  Fault tolerant K-center problems , 1997, Theor. Comput. Sci..

[54]  Mark Jerrum,et al.  The Swendsen-Wang process does not always mix rapidly , 1997, STOC '97.

[55]  David R. Karger,et al.  Approximate graph coloring by semidefinite programming , 1998, JACM.

[56]  Kamal Jain,et al.  A Factor 2 Approximation Algorithm for the Generalized Steiner Network Problem , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[57]  Rajmohan Rajaraman,et al.  Analysis of a local search heuristic for facility location problems , 2000, SODA '98.

[58]  Daniele Micciancio,et al.  The shortest vector in a lattice is hard to approximate to within some constant , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[59]  Milena Mihail Set Cover with Requirements and Costs Evolving over Time , 1999, RANDOM-APPROX.

[60]  Venkatesan Guruswami,et al.  Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems , 1999, STOC '99.

[61]  Vijay V. Vazirani,et al.  On the bidirected cut relaxation for the metric Steiner tree problem , 1999, SODA '99.

[62]  Eric Vigoda,et al.  Improved bounds for sampling colorings , 1999, 40th Annual Symposium on Foundations of Computer Science (Cat. No.99CB37039).

[63]  Vijay V. Vazirani,et al.  Primal-Dual Schema Based Approximation Algorithms , 2000, Theoretical Aspects of Computer Science.

[64]  László Lovász,et al.  The cover time, the blanket time, and the Matthews bound , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[65]  Vijay V. Vazirani,et al.  An approximation algorithm for the fault tolerant metric facility location problem , 2000, APPROX.

[66]  Vijay V. Vazirani,et al.  Approximation algorithms for metric facility location and k-Median problems using the primal-dual schema and Lagrangian relaxation , 2001, JACM.

[67]  Siam Staff A 2-Approximation Algorithm for the Directed Multiway Cut Problem , 2002 .

[68]  George Markowsky,et al.  A fast algorithm for Steiner trees , 1981, Acta Informatica.