Computing Almost Shortest Paths

ACM Transactions on Algorithms

Volumn 1, Issue 2, 2005, Pages 283-323

  Elkin, Michael ^a,b  

^a Yale University   (United States)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Algorithms; Almost shortest paths; Graph algorithms; Spanners; Theory

Indexed keywords

EID: 85016166786     PISSN: 15496325     EISSN: 15496333     Source Type: Journal    
DOI: 10.1145/1103963.1103968     Document Type: Article

References (29)

1. Billingsley, P. 1968. Convergence of Probability Measures. Wiley, New York.
2. Borel, E. 1942. Sur l'emploi du theoreme de Bernoulli pour faciliter le calcul d'une infinite de coefficients. Application au probleme de l'attente a un guichet. C. R. Acad. Sci. Paris 214, 452-456.
3. Carlsson, S., Munro, J. I., and Poblete, P. V. 1987. On linear probing hashing. Unpublished manuscript.
4. Celis, P., Larson, P.-A., and Munro, J. I. 1985. Robin Hood hashing (preliminary report). In Proceedings 26th Annual Symposium on Foundations of Computer Science (FOCS'85) (Portland, OR). IEEE Computer Society Press, Los Alamitos, CA, 281-288.
5. Chassaing, P., and Louchard, G. 2002. Phase transition for parking blocks, Brownian excursion and coalescence. Random Struct. Alg. 21, 1, 76-119.
6. Dwass, M. 1969. The total progeny in a branching process and a related random walk. J. Appl. Probab. 6, 682-686.
7. Flajolet, P., Poblete, P., and Viola, A. 1998. On the analysis of linear probing hashing. Algorithmica 22, 4, 490-515.
8. Graham, R. L., Knuth, D. E., and Patashnik, O. 1994. Concrete Mathematics, 2nd ed. Addison-Wesley, Reading, MA.
9. Janson, S. 2001a. Asymptotic distribution for the cost of linear probing hashing. Random Struct. Alg. 19, 3-4, 438-471.
10. Janson, S. 2001b. Moment convergence in conditional limit theorems. J. Appl. Probab. 38, 2, 421-437.
11. Kemperman, J. H. B. 1950. The General One-Dimensional Random Walk with Absorbing Barriers with Applications to Sequential Analysis. Excelsiors Foto-Offset, the Hague, the Netherlands. Ph.D. thesis.
12. Kemperman, J. H. B. 1961. The Passage Problem for a Stationary Markov Chain. University of Chicago Press, Chicago, IL.
13. Kendall, D. G. 1951. Some problems in the theory of queues. J. Roy. Statist. Soc. Ser. B. 13, 151-185.
14. Knuth, D. E. 1963. Notes on “open” addressing. Unpublished notes, available at http://www.wits.ac.za/helmut/first.ps.
15. Knuth, D. E. 1998a. The Art of Computer Programming. Vol. 3: Sorting and Searching, 2nd ed. Addison-Wesley, Reading, MA.
16. Knuth, D. E. 1998b. Linear probing and graphs. Algorithmica 22, 4, 561-568.
17. Kolchin, V. F. 1984. Random Mappings. Nauka, Moscow. (Russian). English transl.: Optimization Software, New York, 1986.
18. Otter, R. 1949. The multiplicative process. Ann. Math. Statist. 20, 206-224.
19. Pavlov, Yu. L. 1977. The asymptotic distribution of maximum tree size in a random forest. Teor. Verojatnost. i Primenen. 22, 3, 523-533.
20. Pavlov, Yu. L. 1996. Random forests. Karelian Centre Russian Acad. Sci., Petrozavodsk. (Russian). English transl.: VSP, Zeist, the Netherlands, 2000.
21. Pitman, J. 1998. Enumerations of trees and forests related to branching processes and random walks. In Microsurveys in Discrete Probability (Princeton, NJ, 1997). Number 41 in DIMACS Ser. Discrete Math. Theoret. Comput. Sci., American Mathmatics Society, Providence, RI, 163-180.
22. Poblete, P. V., and Munro, J. I. 1989. Last-come-first-served hashing. J. Algorithms 10, 2, 228-248.
23. Poblete, P. V., Viola, A., and Munro, J. I. 1997a. Analyzing the LCFS linear probing hashing algorithm with the help of Maple. MapleTech 4, 1, 8-13.
24. Poblete, P. V., Viola, A., and Munro, J. I. 1997b. The diagonal Poisson transform and its application to the analysis of a hashing scheme. Random Struct. Alg. 10, 1-2, 221-255.
25. Takacs, L. 1967. Combinatorial Methods in the Theory of Stochastic Processes. Wiley, New York.
26. Takacs, L. 1989. Ballots, queues and random graphs. J. Appl. Probab. 26, 1, 103-112.
27. Tanner, J. C. 1961. A derivation of the Borel distribution. Biometrika 48, 222-224.
28. Viola, A. 1995. Analysis of hashing algorithms and a new mathematical transform. Ph.D. thesis, Technical report CS-95-50, Computer Science Department, University of Waterloo, Waterloo, ON, Canada.
29. Viola, A. 2005. Exact distributions of individual displacements in linear probing hashing. ACM Trans. Algorithms 1, 2, 214-242.