Advertisement

A near optimal algorithm for the extended cow-path problem in the presence of relative errors

  • Pallab Dasgupta
  • P. P. Chakrabarti
  • S. C. DeSarkar
Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1026)

Abstract

In classical path finding problems, the cost of a search function is simply the number of queries made to an oracle that knows the position of the goal. In many problems, we want to charge a cost proportional to the distance between queries (e.g., the time required to travel between two query points). With this cost function in mind, the original w-lane cow-path problem [8] was modeled as a navigation problem in a terrain which consists of w-concurrent avenues. In this paper we study a variant of this problem where the terrain is an uniform b-ary tree, and there is a lower-bound estimate of the cost function. We present a strategy CowP for this class of problems where the relative error is bounded by a known constant and show that its worst case complexity is less than or equal to [4b/(b−1)] times optimal.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Baeza-Yates, R. A., J.C.Culberson, and G.J.E.Rawlins. Searching in the plane. Information and Computation 106 (1993), 234–252.Google Scholar
  2. 2.
    Blum, A., P.Raghavan, and B.Schieber. Navigating in unfamiliar geometric terrains. In STOC (1991), pp. 494–504.Google Scholar
  3. 3.
    Dasgupta, P., P.P.Chakrabarti, and S.C.DeSarkar. Agent searching in a tree and the optimality of iterative deepening. Artificial Intelligence 71 (1994), 195–208.Google Scholar
  4. 4.
    Dechter, R., and J.Pearl. Generalized best-first search strategies and the optimality of A *. JACM 32, 3 (1985), 505–536.Google Scholar
  5. 5.
    Fiat, A., D.P.Foster, H.Karloff, Y.Rabani, Y.Ravid, and S.Vishwanathan. Competitive algorithms for layered graph traversal. In FOCS (1991), pp. 288–297.Google Scholar
  6. 6.
    Fiat, A., Y.Rabani, and Y.Ravid. Competitive k-server algorithms. In FOCS (1990), pp. 454–463.Google Scholar
  7. 7.
    Ghosh, S. K., and S.Saluja. Optimal on-line algorithms for walking with minimum number of turns in unknown streets. Tech. Rep. TCS-94/2, TIFR, Bombay, 1994.Google Scholar
  8. 8.
    Kao, M. Y., J.H.Reif, and S.R.Tate. Searching in an unknown environment: An optimal randomized algorithm for the cow-path problem. In SODA (1992), pp. 441–447.Google Scholar
  9. 9.
    Karp, R. M., M.Saks, and A.Widgerson. On a search problem related to branchand-bound procedures. In Proc. of 27th Annual Symp. on Foundations of Computer Science (1986), pp. 19–28.Google Scholar
  10. 10.
    Klein, R. Walking an unknown street with bounded detour. Computational Geometry: Theory and Applications 1 (1992), 325–351.Google Scholar
  11. 11.
    Kleinberg, J. M. On-line search in a simple polygon. In Proc. of SODA'94 (1994), pp. 8–15.Google Scholar
  12. 12.
    Korf, R. E. Depth-first iterative deepening: An optimal admissible tree search. Artificial Intelligence 27 (1985), 97–109.Google Scholar
  13. 13.
    Papadimitriou, C. H. Shortest path motion. In Proc. FST-TCS Conference, New Delhi (1987).Google Scholar
  14. 14.
    Papadimitriou, C. H., and M.Yannakakis. Shortest paths without a map. Theoretical Computer Science 84 (1991), 127–150.Google Scholar
  15. 15.
    Pearl, J. Heuristics: Intelligent Search Strategies for Computer Problem Solving. Addison Wesley, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Pallab Dasgupta
    • 1
  • P. P. Chakrabarti
    • 1
  • S. C. DeSarkar
    • 1
  1. 1.Dept. of Computer Sc & Engg.Indian Institute of TechnologyKharagpurIndia

Personalised recommendations