Abstract
A familiar quandary arises when there are several possible alternatives for the solution of a problem, but no way of knowing which, if any, are viable for a particular problem instance. Faced with this uncertainty, one is forced to simulate the parallel exploration of alternatives through some kind of co-ordinated interleaving (dovetailing) process. As usual, the goal is to find a solution with low total cost. Much of the existing work on such problems has assumed, implicitly or explicitly, that at most one of the alternatives is viable, providing support for a competitive analysis of algorithms (using the cost of the unique viable alternative as a benchmark). In this paper, we relax this worst-case assumption in revisiting several familiar dovetailing problems.
Our main contribution is the introduction of a novel process interleaving technique, called hyperbolic dovetailing that achieves a competitive ratio that is within a logarithmic factor of optimal on all inputs in the worst, average and expected cases, over all possible deterministic (and randomized) dovetailing schemes. We also show that no other dovetailing strategy can guarantee an asymptotically smaller competitive ratio for all inputs.
An interesting application of hyperbolic dovetailing arises in the design of what we call input-thrifty algorithms, algorithms that are designed to minimize the total precision of the input requested in order to evaluate some given predicate. We show that for some very basic predicates involving real numbers we can use hyperbolic dovetailing to provide input-thrifty algorithms that are competitive, in this novel cost measure, with the best algorithms that solve these problems.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Azar, Y., Broder, A.Z., Manasse, M.S.: On-line choice of on-line algorithms. In: Proc. 4th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 432–440 (1993)
Baeza-Yates, R.A., Culberson, J.C., Rawlins, G.J.E.: Searching in the plane. Information and Computation 106(2), 234–252 (1993)
Ben-David, S., Borodin, A.: A new measure for the study of on-line algorithms. Algorithmica 11, 73–91 (1994)
Boyar, J., Favrholdt, L.M.: The relative worst order ratio for on-line algorithms. ACM Trans. on Algorithms 3(2) (2007)
Boyar, J., Favrholdt, L.M., Larsen, K.S.: The relative worst order ratio applied to paging. In: Proc. 16th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 718–727 (2005)
Demaine, E., Fekete, S., Gal, S.: Online searching with turn cost. Theoretical Computer Science 361, 342–355 (2006)
Dorrigiv, R., Lopez-Ortiz, A.: A survey of performance measures for on-line algorithms. ACM SIGACT News 36(3), 67–81 (2005)
Kao, M.-Y., Littman, M.L.: Algorithms for informed cows. In: AAAI 1997 Workshop on On-Line Search (1997)
Kao, M.-Y., Ma, Y., Sipser, M., Yin, Y.: Optimal constructions of hybrid algorithms. J. Algorithms 29(1), 142–164 (1998)
Kao, M.-Y., Reif, J.H., Tate, S.R.: Searching in an unknown environment: An optimal randomized algorithm for the cow-path problem. Information and Computation 131(1), 63–79 (1996)
Kenyon, C.: Best-fit bin-packing with random order. In: Proc. 7th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 359–364 (1996)
Koutsoupias, E., Papadimitriou, C., Yannakakis, M.: Searching a fixed graph. In: Proc. 23rd International Colloquium on Automata, Languages and Programming, pp. 280–289 (1996)
Lopez-Ortiz, A., Schuierer, S.: The ultimate strategy to search on m rays. Theoretical Computer Science 2(28), 267–295 (2001)
Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. In: Proc. Second Israel Symposium on Theory of Computing and Systems, June 1993, pp. 128–133 (1993)
Papadimitriou, C.H., Yannakakis, M.: Shortest path without a map. In: Proc. 16th International Colloquium on Automata, Languages and Programming, pp. 610–620 (1989)
Schonhage, A.: Adaptive raising strategies optimizing relative efficiency. In: Proc. 30th International Colloquium on Automata, Languages and Programming, pp. 611–623 (2003)
Schuierer, S.: Lower bounds in on-line geometric searching. Computational Geometry: Theory and Applications 18(1), 37–53 (2001)
Schuierer, S.: A lower bound for randomized searching on m rays. In: Klein, R., Six, H.-W., Wegner, L. (eds.) Computer Science in Perspective. LNCS, vol. 2598, pp. 264–277. Springer, Heidelberg (2003)
Sleator, D.D., Tarjan, R.E.: Amortized efficiency of list update and paging rules. Comm. ACM, 202–208 (February 1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kirkpatrick, D. (2009). Hyperbolic Dovetailing. In: Fiat, A., Sanders, P. (eds) Algorithms - ESA 2009. ESA 2009. Lecture Notes in Computer Science, vol 5757. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04128-0_46
Download citation
DOI: https://doi.org/10.1007/978-3-642-04128-0_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04127-3
Online ISBN: 978-3-642-04128-0
eBook Packages: Computer ScienceComputer Science (R0)