No CrossRef data available.
Article contents
A survey on combinatorial optimizationin dynamic environments∗
Published online by Cambridge University Press: 16 December 2011
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.
This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The second framework is probabilistic optimization, where the instance to optimize is not fully known at the time when a solution is to be proposed, but results from a determined Bernoulli process. Then, the goal is to compute a solution with optimal expected value.
Keywords
Information
- Type
- Research Article
- Information
- Copyright
- © EDP Sciences, ROADEF, SMAI 2011
References
Références
S. Albers, On randomized online scheduling, in Proceedings of the thiry-fourth annual ACM symposium on Theory of computing, ACM (2002) 134–143.
Archetti, C., Bertazzi, L. and Speranza, M.G., Reoptimizing the traveling salesman problem. Networks 42 (2003) 154–159. Google Scholar
Archetti, C., Bertazzi, L. and Speranza, M.G., Reoptimizing the 0-1 knapsack problem. Discrete Appl. Math. 158 (2010) 1879–1887. Google Scholar
T. Asano, K. Hori, T. Ono and T. Hirata, A theoretical framework of hybrid approaches to max sat, in ISAAC, Lecture Notes in Computer Science 1350, edited by H.W. Leong, H. Imai and S. Jain. Springer (1997) 153–162.
Ausiello, G., Italiano, G.F., Marchetti-Spaccamela, A. and Nanni, U., Incremental algorithms for minimal length paths. J. Algorithms 12 (1991) 615–638. Google Scholar
Ausiello, G., Feuerstein, E., Leonardi, S., Stougie, L. and Talamo, M., Algorithms for the on-line traveling salesman problem. Algorithmica 29 (2001) 560–581. Google Scholar
G. Ausiello, B. Escoffier, J. Monnot and V.Th. Paschos, Reoptimization of minimum and maximum traveling salesman’s tours, in SWAT, Lecture Notes in Computer Science 4059, edited by L. Arge and R. Freivalds. Springer (2006) 196–207.
Ausiello, G., Escoffier, B., Monnot, J. and Paschos, V.Th., Reoptimization of minimum and maximum traveling salesman’s tours. J. Discrete Algorithms 7 (2009) 453–463. Google Scholar
G. Ausiello, V. Bonifaci and B. Escoffier, Complexity and approximation in reoptimization. Cahier du LAMSADE 281. Université Paris-Dauphine (2008).
Averbakh, I. and Berman, O., Probabilistic sales-delivery man and sales-delivery facility location problems on a tree. Transp. Sci. 29 (1995) 184. Google Scholar
Averbakh, I., Berman, O. and Simchi-Levi, D., Probabilistic a priori routing-location problems. Nav. Res. Logist. 41 (1994) 973–989. Google Scholar
Bar-Yehuda, R. and Even, S., A linear-time approximation algorithm for the weighted vertex cover problem. J. Algorithms 2 (1981) 198–203. Google Scholar
Bartusch, M., Möhring, R.H. and Radermacher, F.J., A conceptional outline of a DSS for scheduling problems in the building industry. Decis. Support Syst. 5 (1989) 321–344. Google Scholar
Bartusch, M., Möhring, R.H. and Radermacher, F.J., Design aspects of an advanced model-oriented DSS for scheduling problems in civil engineering. Decis. Support Syst. 5 (1989) 321–344. Google Scholar
J. Beardwood, J.H Halton and J.M Hammersley, The shortest path through many points, in Mathematical Proceedings of the Cambridge Philosophical Society 55. Cambridge Univ Press (1959) 299–327.
M. Bellalouna, Problèmes d’optimisation combinatoires probabilistes. Ph.D. thesis, École Nationale des Ponts et Chaussées, Paris, France (1993).
M. Bellalouna, S. Souissi and B. Ycart, Average-Case Analysis for the Probabilistic Bin Packing Problem, in Mathematics and Computer Science III: Algorithms, Trees, Combinatorics and Probabilities (2004) 149–159.
Bern, M. and Plassmann, P., The Steiner problem with edge lengths 1 and 2. Inf. Proc. Lett. 32 (1989) 171–176. Google Scholar
Berenguer, X., A characterization of linear admissible transformations for the m-travelling salesmen problem. Eur. J. Oper. Res. 3 (1979) 232–238. Google Scholar
D.J. Bertsimas, Probabilistic combinatorial optimization problems. Ph.D. thesis, Massachusetts Institute of Technology (1988).
Bertsimas, D.J., Traveling salesman facility location problems. Transp. Sci. 23 (1989) 184. Google Scholar
Bertsimas, D.J., The probabilistic minimum spanning tree problem. Networks 20 (1990) 245–275. Google Scholar
Bertsimas, D.J., A vehicle routing problem with stochastic demand. Oper. Res. 40 (1992) 574–585. Google Scholar
Bertsimas, D.J. and Simchi-Levi, D., A new generation of vehicle routing research: robust algorithms, addressing uncertainty. Oper. Res. 44 (1996) 286–304. Google Scholar
Bertsimas, D.J., Jaillet, P. and Odoni, A.R., A priori optimization. Oper. Res. 38 (1990) 1019–1033. Google Scholar
Bertsimas, D.J., Jaillet, P. and Odoni, A.R., A priori optimization. Oper. Res. 38 (1990) 1019–1033. Google Scholar
D. Bilò, H.-J. Böckenhauer, J. Hromkovic, R. Královic, T. Mömke, P. Widmayer and A. Zych. Reoptimization of steiner trees, in SWAT, Lecture Notes in Computer Science 5124, edited by J. Gudmundsson. Springer (2008) 258–269.
D. Bilò, P. Widmayer and A. Zych, Reoptimization of weighted graph and covering problems, in WAOA, Lecture Notes in Computer Science 5426, edited by E. Bampis and M. Skutella. Springer (2008) 201–213.
D. Bilò, H.-J. Böckenhauer, D. Komm, R. Královic, T. Mömke, S. Seibert and A. Zych, Reoptimization of the shortest common superstring problem, in CPM, Lecture Notes Computer Science 5577, edited by G. Kucherov and E. Ukkonen. Springer (2009) 78–91.
Blom, M., Krumke, S., De Paepe, W. and Stougie, L., The online-TSP against fair adversaries. Algorithms and Complexity (2000) 137–149. Google Scholar
Böckenhauer, H.-J. and Komm, D., Reoptimization of the metric deadline TSP. J. Discrete Algorithms 8 (2010) 87–100. Google Scholar
H.-J. Böckenhauer, L. Forlizzi, J. Hromkovic, J. Kneis, J. Kupke, G. Proietti and P. Widmayer, Reusing optimal TSP solutions for locally modified input instances, in IFIP TCS IFIP 209, edited by G. Navarro, L.E. Bertossi and Y. Kohayakawa. Springer (2006) 251–270.
Böckenhauer, H.-J., Forlizzi, L., Hromkovic, J., Kneis, J., Kupke, J., Proietti, G. and Widmayer, P., On the approximability of TSP on local modifications of optimally solved instances. Algorithmic Operations Research 2 (2007) 83–93. Google Scholar
H.-J. Böckenhauer, J. Hromkovic, T. Mömke and P. Widmayer, On the hardness of reoptimization, in SOFSEM, Lecture Notes in Computer Science 4910, edited by V. Geffert, J. Karhumäki, A. Bertoni, B. Preneel, P. Návrat and M. Bieliková. Springer (2008) 50–65.
Böckenhauer, H.-J., Hromkovic, J., Královic, R., Mömke, T. and Rossmanith, P., Reoptimization of steiner trees: Changing the terminal set. Theor. Comput. Sci. 410 (2009) 3428–3435. Google Scholar
H.-J. Böckenhauer, K. Freiermuth, J. Hromkovic, T. Mömke, A. Sprock and B. Steffen, The steiner tree reoptimization problem with sharpened triangle inequality, in CIAC, Lecture Notes in Computer Science 6078, edited by T. Calamoneri and J. Díaz. Springer (2010) 180–191.
Boria, N. and Paschos, V.T., Fast reoptimization for the minimum spanning tree problem. J. Discrete Algorithms 8 (2010) 296–310. Google Scholar
N. Boria, C. Murat and V.T. Paschos, On the probabilistic min spanning tree problem, in IMCSIT (2010) 893–900.
N. Boria, J. Monnot and V. Th. Paschos, Reoptimization of maximum weight induced hereditary subgraph problems. Cahier du LAMSADE 311, LAMSADE, Université Paris-Dauphine (2011).
N. Boria, J. Monnot and V. Th. Paschos, Reoptimization of the maximum weight P k-free subgraph under vertex insertion, in Proc. Workshop on Algorithms and Computation, WALCOM’12, Lect. Notes Comput. Sci. Springer-Verlag (2011), to appear.
N. Boria, C. Murat and V. Th. Paschos, On the probabilistic min spanning tree problem. J. Mathematical Modelling and Algorithms. To appear.
Bourgeois, N., Della Croce, F., Escoffier, B., Murat, C. and Paschos, V.Th., Probabilistic graph-coloring in bipartite and split graphs. J. Combin. Optim. 17 (2009) 274–311. Google Scholar
Bouyahia, Z., Bellalouna, M., Jaillet, P. and Ghedira, K., A priori parallel machines scheduling. Comput. Ind. Eng. 58 (2010) 488–500. Google Scholar
K. Chaudhuri, B. Godfrey, S. Rao and K. Talwar, Paths, trees, and minimum latency tours, in FOCS. IEEE Computer Society (2003) 36–45.
N. Christofides, Worst-case analysis of a new heuristic for the travelling salesman problem. Technical Report 388, Graduate School of Industrial Administration, Carnegie Mellon University (1976).
Demange, M. and Paschos, V.T., On-line vertex-covering. Theor. Comput. Sci. 332 (2005) 83–108. Google Scholar
M. Demange and B. Leroy-Beaulieu, Online coloring of comparability graphs: some results. Report, Chair ROSE-2007-001, École Polytechnique Fédérale de Lausanne (2007).
M. Demange, X. Paradon and V.Th. Paschos, On-line maximum-order induced hereditary subgraph problems, in SOFSEM 2000 – Theory and Practice of Informatics, Lecture Notes in Computer Science 1963, edited by V. Hlavcáˇ, K. G. Jeffery and J. Wiedermann. Springer-Verlag (2000) 326–334.
Demange, M., Paradon, X. and Paschos, V.Th., On-line maximum-order induced hereditary subgraph problems. Int. Trans. Operat. Res. 12 (2005) 185–201. Google Scholar
M. Demange, G. Di Stefano and B. Leroy-Beaulieu, On the online track assignment problem. Discrete Appl. Math. To appear.
Demetrescu, C. and Italiano, G.F., A new approach to dynamic all pairs shortest paths. J. ACM 51 (2004) 968–992. Google Scholar
Dertouzos, M.L. and Mok, A.K., Multiprocessor online scheduling of hard-real-time tasks. IEEE Trans. Softw. Eng. 15 (2002) 1497–1506. Google Scholar
Eppstein, D., Galil, Z., Italiano, G.F. and Nissenzweig, A., Sparsification – a technique for speeding up dynamic graph algorithms. J. ACM 44 (1997) 669–696. Google Scholar
Escoffier, B., Milanic, M. and Paschos, V.Th., Simple and fast reoptimizations for the steiner tree problem. Algorithmic Operations Research 4 (2009) 86–94. Google Scholar
Even, S. and Gazit, H., Updating distances in dynamic graphs. Methods Oper. Res. 49 (1985) 371–387. Google Scholar
U. Feige and M. Singh, Improved approximation ratios for traveling salesperson tours and paths in directed graphs, in APPROX-RANDOM, Lecture Notes in Computer Science 4627, edited by M. Charikar, K. Jansen, O. Reingold and J.D.P. Rolim. Springer (2007) 104–118.
Frederickson, G.N., Data structures for on-line updating of minimum spanning trees, with applications. SIAM J. Comput. 14 (1985) 781–798. Google Scholar
Frederickson, G.N., Ambivalent data structures for dynamic 2-edge-connectivity and k smallest spanning trees. SIAM J. Comput. 26 (1997) 484–538. Google Scholar
Frieze, A.M., On the value of a random minimum spanning tree problem. Discrete Appl. Math. 10 (1985) 47–56. Google Scholar
Frieze, A.M., Galbiati, G. and Maffioli, F., On the worst-case performance of some algorithms for the asymmetric traveling salesman problem. Networks 12 (1982) 23–39. Google Scholar
Frigioni, D., Marchetti-Spaccamela, A. and Nanni, U., Fully dynamic algorithms for maintaining shortest paths trees. J. Algorithms 34 (2000) 251–281. Google Scholar
Gabrel, V., Moulet, A., Murat, C. and Paschos, V.T., A new single model and derived algorithms for the satellite shot planning problem using graph theory concepts. A. Oper. Res. 69 (1997) 115–134. Google Scholar
Gallant, J., Maier, D. and Storer, J.A., On finding minimal length superstrings. J. Comput. Syst. Sci. 20 (1980) 50–58. Google Scholar
Hall, N.G. and Posner, M.E., Sensitivity analysis for scheduling problems. J. Scheduling 7 (2004) 49–83. Google Scholar
M.M. Halldórsson, Online coloring known graphs, in Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms, Society for Industrial and Applied Mathematics (1999) 918.
Halldórsson, M.M. and Radhakrishnan, J., Greed is good: Approximating independent sets in sparse and bounded-degree graphs. Algorithmica 18 (1997) 145–163. Google Scholar
Halldórsson, M.M., Iwama, K., Miyazaki, S. and Taketomi, S., Online independent sets. Theor. Comput. Sci. 289 (2002) 953–962. Google Scholar
Hassin, R. and Rubinstein, S., A 7/8-approximation algorithm for metric Max TSP. Inf. Proc. Lett. 81 (2002) 247–251. Google Scholar
Henzinger, M.R., Improved data structures for fully dynamic biconnectivity. SIAM J. Comput. 29 (2000) 1761–1815. Google Scholar
M.R. Henzinger and V. King, Fully dynamic biconnectivity and transitive closure, in FOCS. IEEE Computer Society (1995) 664–672.
M.R. Henzinger and V. King, Maintaining minimum spanning trees in dynamic graphs, in ICALP, Lecture Notes in Computer Science 1256, edited by P. Degano, R. Gorrieri and A. Marchetti-Spaccamela. Springer (1997) 594–604.
Henzinger, M.R. and King, V., Randomized fully dynamic graph algorithms with polylogarithmic time per operation. J. ACM 46 (1999) 502–516. Google Scholar
M.R. Henzinger and J.A. La Poutré, Certificates and fast algorithms for biconnectivity in fully-dynamic graphs, in ESA, Lecture Notes in Computer Science 979, edited by P.G. Spirakis. Springer (1995) 171–184.
Holm, J., de Lichtenberg, K. and Thorup, M., Poly-logarithmic deterministic fully-dynamic algorithms for connectivity, minimum spanning tree, 2-edge, and biconnectivity. J. ACM 48 (2001) 723–760. Google Scholar
L. Horchani and M. Bellalouna, The 2-dimensional probabilistic bin packing problem: an average case analysis of the FBS algorithm, in Proceedings of the American Conference on Applied Mathematics. World Scientific and Engineering Academy and Society (WSEAS) (2008) 449–453.
Ibarra, O.H. and Kim, C.E., Fast approximation algorithms for the knapsack and sum of subset problems. J. ACM 22 (1975) 463–468. Google Scholar
Z. Ivković and E.L. Lloyd, Fully dynamic maintenance of vertex cover, in Graph-Theoretic Concepts in Computer Science. Springer (1994) 99–111.
Ivković, Z. and Lloyd, E.L., Fully dynamic algorithms for bin packing: Being (mostly) myopic helps. SIAM J. Comput. 28 (1998) 574–611. Google Scholar
P. Jaillet, Probabilistic traveling salesman problems. Ph.D. thesis, Massachusetts Institute of Technology (1985).
Jaillet, P., A priori solution of a traveling salesman problem in which a random subset of the customers are visited. Oper. Res. 36 (1988) 929–936. Google Scholar
Jaillet, P., Analysis of probabilistic combinatorial optimization problems in Euclidean spaces. Math. Oper. Res. 18 (1993) 51–70. Google Scholar
P. Jaillet and A.R. Odoni, The probabilistic vehicle routing problem, in Vehicle routing: Methods and Studies, edited by B.L. Golden and A.A. Assad. North Holland, Amsterdam (1988) 293–318.
Jaillet, P. and Wagner, M.R., Online routing problems: Value of advanced information as improved competitive ratios. Transp. Sci. 40 (2006) 200–210. Google Scholar
D.S. Johnson, Near-optimal bin packing algorithms. Ph.D. thesis, Massachusetts Institute of Technology (1973).
Johnson, D.S., Fast algorithms for bin packing. J. Comput. Syst. Sci. 8 (1974) 272–314. Google Scholar
Johnson, D.S. and Garey, M.R., A 71/60 theorem for bin packing. J. Complex. 1 (1985) 65–106. Google Scholar
N. Karmarkar and R.M. Karp, An efficient approximation scheme for the one-dimensional bin-packing problem, in FOCS, Chicago, IEEE Computer Society Illinois (1982) 312–320.
Karp, R.M., Probabilistic analysis of partitioning algorithms for the traveling-salesman problem in the plane. Math. Oper. Res. 2 (1977) 209–224. Google Scholar
Karp, R.M., A patching algorithm for the nonsymmetric traveling-salesman problem. SIAM J. Comput. 8 (1979) 561. Google Scholar
V. King, Fully dynamic algorithms for maintaining all-pairs shortest paths and transitive closure in digraphs, in FOCS. IEEE Computer Society (1999) 81–91.
Klein, P.N. and Subramanian, S., A fully dynamic approximation scheme for shortest paths in planar graphs. Algorithmica 22 (1998) 235–249. Google Scholar
S.R. Kosaraju, J.K. Park and C. Stein, Long tours and short superstrings (preliminary version), in FOCS. IEEE Computer Society (1994) 166–177.
J.B. Kruskal, On the shortest spanning subtree of a graph and the traveling salesman problem, in Proceedings of the American Mathematical Society 7 (1956).
P.S. Loubal, A network evaluation procedure. Bay Area Transportation Study Commission (1967).
C. Lund and M. Yannakakis, The approximation of maximum subgraph problems, in Proc. ICALP’93, Lecture Notes in Computer Science 700. edited by A. Lingas, R.G. Karlsson and S. Carlsson. Springer-Verlag (1993) 40–51.
Miltersen, P.B., Subramanian, S., Vitter, J.S. and Tamassia, R., Complexity models for incremental computation. Theor. Comput. Sci. 130 (1994) 203–236. Google Scholar
Murat, C. and Paschos, V.Th., The probabilistic longest path problem. Networks 33 (1999) 207–219. Google Scholar
Murat, C. and Paschos, V.Th., A priori optimization for the probabilistic maximum independent set problem. Theor. Comput. Sci. 270 (2002) 561–590. Google Scholar
Murat, C. and Paschos, V.Th., The probabilistic minimum vertex-covering problem. Int. Trans. Oper. Res. 9 (2002) 19–32. Google Scholar
C. Murat and V. Paschos, The probabilistic minimum coloring problem, in Graph-Theoretic Concepts in Computer Science, Springer (2003) 346–357.
Murat, C. and Paschos, V.T., On the probabilistic minimum coloring and minimum k-coloring. Discrete Appl. Math. 154 (2006) 564–586. Google Scholar
C. Murat and V.T. Paschos, Probabilistic combinatorial optimization on graphs. Wiley Online Library (2006).
J. Murchland, The effect of increasing or decreasing the length of a single arc on all shortest distances in a graph. London Businness School, Transport Network Theory Unit (1967).
Papadimitriou, C.H. and Yannakakis, M., The traveling salesman problem with distances one and two. Math. Oper. Res. 18 (1993) 1–11. Google Scholar
Paz, A. and Moran, S., Non deterministic polynomial optimization problems and their approximations. Theor. Comput. Sci. 15 (1981) 251–277. Google Scholar
K. Pruhs, E. Torng and J. Sgall, Online scheduling, in Handbook of Scheduling: Algorithms, Models, and Performance Analysis, edited by Joseph Y.-T. Leung, Chapter 15. CRC Press (2004) 15-1–15-41.
Richey, M.B., Improved bounds for harmonic-based bin-packing algorithms. Discrete Appl. Math. 3 (1991) 203–227. Google Scholar
Robertson, N. and Seymour, P.D., Graph minors. XX. Wagner’s conjecture. J. Comb. Theory, Ser. B 92 (2004) 325–357. Google Scholar
G. Robins and A. Zelikovsky, Improved steiner tree approximation in graphs, in SODA (2000) 770–779.
Rodionov, V.V., The parametric problem of shortest distances. USSR Comput. Math. Math. Phys. 8 (1968) 336–343. Google Scholar
H. Rohnert, A dynamization of the all pairs least cost path problem, in STACS, Lecture Notes in Computer Science 182, edited by K. Mehlhorn. Springer (1985) 279–286.
Sahni, S. and Gonzalez, T.F., P-complete approximation problems. J. ACM 23 (1976) 555–565. Google Scholar
Schäffter, M.W., Scheduling with forbidden sets. Discrete Appl. Math. 72 (1997) 155–166. Google Scholar
Seguin, R., Problèmes stochastiques de tournées de véhicules: un pas de plus vers le réalisme. Cahiers du Centre d’études de recherche opérationnelle 35 (1993) 187–226. Google Scholar
J. Sgall, On-line scheduling-a survey, in Online Algorithms: The State of the Art, edited by A. Fiat and G.J. Woeginger, Lect. Notes Comput. Sci. 1442. Springer (1998) 196–231. (1997).
R. Sitters, The minimum latency problem is np-hard for weighted trees, in IPCO, Lecture Notes in Computer Science 2337, edited by W. Cook and A.S. Schulz. Springer (2002) 230–239.
Sleator, D.D. and Tarjan, R.E., A data structure for dynamic trees. J. Comput. Syst. Sci. 26 (1983) 362–391. Google Scholar
Steele, J.M., Subadditive Euclidean functionals and nonlinear growth in geometric probability. Ann. Probab. 9 (1981) 365–376. Google Scholar
Steele, J.M., On Frieze’s χ(3) limit for lengths of minimal spanning trees. Discrete Appl. Math. 18 (1987) 99–103. Google Scholar
Sweedyk, Z., A 2+1/2-approximation algorithm for shortest superstring. SIAM J. Comput. 29 (1999) 954–986. Google Scholar
Van Vliet, A., An improved lower bound for on-line bin-packing algorithms. Inf. Proc. Lett. 43 (1992) 277–284. Google Scholar
V. Vassilevska, Explicit inapproximability bounds for the shortest superstring problem, in MFCS, Lecture Notes in Computer Science 3618, edited by J. Jedrzejowicz and A. Szepietowski. Springer (2005) 793–800.
You have
Access
- 17
- Cited by