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Abstract: . In the past few years, there has been significant progress in our understanding of the extent to which near-optimal solutions can be efficiently computed for NP-hard combinatorial optimization problems. This paper surveys these recent developments, while concentrating on the advances made in the design and analysis of approximation algorithms, and in particular, on those results that rely on linear programming and its generalizations. In the past few years, there have been major advances in... (Update)
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BibTeX entry: (Update)
D. B. Shmoys, \Computing Near-Optimal Solutions to Combinatorial Optimization Problems," Combinatorial Optimization, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 20, W. Cook and L. Lovasz (eds.), AMS Publications (1995), 355-397. http://citeseer.ist.psu.edu/shmoys95computing.html More
@techreport{ shmoys95computing,
author = "D. B. Shmoys",
title = "Computing near-optimal solutions to combinatorial optimization problems",
address = "Ithaca, NY 14853",
year = "1995",
url = "citeseer.ist.psu.edu/shmoys95computing.html" }
Citations (may not include all citations):951 Computational complexity (context) - Papadimitriou - 1994 ACM
403 Proof verification and hardness of approximation problems - Arora, Lund et al. - 1992 DBLP
300 the hardness of approximating minimization problems (context) - Lund, Yannakakis - 1993
293 Approximation algorithms for combinatorial problems (context) - Johnson ACM DBLP
242 Non-deterministic exponential time has twoprover interactive.. - Babai, Fortnow et al. - 1991
219 and complexity classes (context) - Papadimitriou, Yannakakis et al. - 1991
203 Approximating clique is almost NP-complete (context) - Feige, Goldwasser et al. - 1991
186 Randomized rounding: a technique for provably good algorithm.. (context) - Raghavan, Thompson - 1987 ACM DBLP
170 Bounds for certain multiprocessing anomalies (context) - Graham - 1966
168 An approximate max-flow min-cut theorem for uniform multicom.. (context) - Leighton, Rao - 1988 DBLP
160 A general approximation technique for constrained forest pro.. - Goemans, Williamson - 1992 ACM DBLP
144 The NP-completeness column: an ongoing guide (context) - Johnson - 1992 ACM DBLP
126 Efficient probabilistically checkable proofs and application.. - Bellare, Goldwasser et al. - 1993
108 Improved non-approximability results - Bellare, Sudan - 1994 ACM DBLP
107 complete approximation problems (context) - Sahni, Gonzalez - 1976
104 Approximating maximum independent sets by excluding subgraph.. - Boppana, Halld'orsson - 1992 ACM DBLP
101 the ratio of optimal integral and fractional covers (context) - Lov'asz - 1975
88 The traveling salesman problem with distances one and two (context) - Papadimitriou, Yannakakis - 1993 ACM
87 Approximation algorithms for scheduling unrelated parallel m.. (context) - Lenstra, Shmoys et al. - 1990 ACM DBLP
85 the approximation of maximum satisfiability (context) - Yannakakis - 1992
84 an estimate of the chromatic class of a p-graph (context) - Vizing - 1964
83 The NP-completeness of edge-coloring (context) - Holyer - 1981 DBLP
79 When trees collide: an approximation algorithm for the gener.. - Agrawal, Klein et al. - 1991
75 Approximation algorithms for set covering and vertex cover p.. (context) - Hochbaum - 1982
71 Vertex packing: structural properties and algorithms (context) - Nemhauser, Trotter - 1975
71 Maximal flow through a network (context) - Ford, Fulkerson - 1956
69 Two-prover one-round proof systems: their power and their pr.. (context) - Feige, Lov'asz - 1992
69 A greedy heuristic for the set covering problem (context) - Chv'atal - 1979
68 Steiner minimal trees (context) - Gilbert, Pollak - 1968
67 Optimal algorithms for approximate clustering (context) - Feder, Greene - 1988 ACM DBLP
63 the complexity of approximating the independent set problem (context) - Berman, Schnitger - 1992
62 the hardness of approximating the chromatic number - Khanna, Linial et al. - 1993
61 A primal-dual approximation algorithm for generalized Steine.. (context) - Williamson, Goemans et al. - 1993 ACM DBLP
59 Improved approximations for the Steiner tree problem (context) - Berman, Ramaiyer - 1992 ACM DBLP
53 An efficient approximation scheme for the onedimensional bin.. (context) - Karmarkar, Karp - 1982
52 An analysis of several heuristics for the traveling salesman.. (context) - Rosenkrantz, Stearns - 1977 DBLP
51 The complexity of scheduling under precedence constraints (context) - Lenstra, Kan - 1978
50 On steiner minimal trees with rectilinear distance (context) - Hwang - 1976
46 Improved approximation algorithms for network design problem.. - Goemans, Goldberg et al. - 1994 ACM DBLP
45 Approximationthrough multicommodity flow (context) - Klein, Agrawal et al. - 1990
42 Worst case analysis of a new heuristic for the travelling sa.. (context) - Christofides - 1976
41 Fast algorithms for bin-packing (context) - Johnson
39 ffl-approximations with minimum packing constraint violation (context) - Lin, Vitter - 1992
38 A still better performance guarantee for approximate graph c.. (context) - Halld'orsson - 1993 ACM DBLP
37 Probabilistic checking of proofs (context) - Arora, Safra - 1992 ACM
35 Biconnectivity approximations and graph carvings - Khuller, Vishkin - 1992 ACM DBLP
34 The complexity of near-optimal graph coloring (context) - Garey, Johnson - 1976 ACM DBLP
34 Improving the performance guarantee for approximate graph co.. (context) - Wigderson - 1983 ACM DBLP
31 the worst-case performance of some algorithms for the asymme.. (context) - Frieze, Galbiati et al. - 1982
30 A linear time approximationalgorithm for the weighted vertex.. (context) - Bar-Yehuda, Even - 1981
28 An efficient approximation algorithm for the survivable netw.. - Gabow, Goemans et al. - 1993 DBLP
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24 On better heuristic for Euclidean Steiner minimum trees (context) - Du, Zhang et al. - 1991
21 Analyzing the Held-Karp TSP bound: a monotonicity property w.. (context) - Shmoys, Williamson - 1990 ACM DBLP
20 A simple heuristic for the p-center problem (context) - Dyer, Frieze - 1985
20 Worst case behavior of graph coloring algorithms (context) - Johnson
20 Algorithms for approximate graph coloring - Blum - 1991 ACM
20 Approximating the minimum degree spanning tree to within one.. (context) - Furer, Raghavachari - 1992 ACM DBLP
17 A near optimal algorithm for edge separators (context) - Chung, Yau - 1994
16 A best possible approximation algorithm for the k-center pro.. (context) - Hochbaum, Shmoys - 1985
16 approximation algorithm for MAX SAT - Goemans, Williamson et al. - 1993
11 Analysis of a linear programming heuristic for scheduling un.. (context) - Potts - 1985
11 878-approximation algorithm for MAX CUT and MAX 2SAT (context) - Goemans, Williamson - 1994
10 The Steiner problem with edge lengths 1 and 2 (context) - Bern, Plassman - 1989 DBLP
10 Easy and hard bottleneck location problems (context) - Hsu, Nemhauser - 1979
9 Scheduling multiple variable-speed machines - Trick - 1991 ACM DBLP
8 A scaling technique for better network design (context) - Aggarwal, Garg - 1994 ACM DBLP
7 An approach for proving lower bounds: solution of Gilbert-Po.. (context) - Du, Hwang - 1990 DBLP
5 An improved approximation algorithm for the generalized assi.. (context) - Shmoys, Tardos - 1993
3 A simple proof of the inequality FFD (context) - Yue - 1991
3 Bin packing can be solved within 1 + ffl in linear time (context) - de la, Lueker - 1981
2 Approximate min-max theorems and fast approximation algorith.. (context) - Tardos - 1993
2 Approximate max-flow min (context) - Garg, Vazirani et al. - 1993
2 Survivable networks (context) - Goemans, Bertsimas - 1993 ACM
2 Methods for integer programming: algebraic (context) - Balinski, Spielberg - 1969
1 The trim problem (context) - Eisemann - 1957 DBLP
1 School of Operations Research and Industrial Engineering (context) - Zelikovsky, -approximationalgorithm et al. - 1993
1 Notes on covering of arcs by nodes in an undirected graph (context) - Lorentzen - 1966
1 Heuristic analysis (context) - Wolsey - 1980
1 Generalized first-order spectra (context) - Fagin - 1974
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