Optimal Constructions of Hybrid Algorithms

Abstract

We study on-line strategies for solving problems with hybrid algorithms. There is a problem Q and w basic algorithms for solving Q. For some λ ≤ w, we have a computer with λ disjoint memory areas, each of which can be used to run a basic algorithm and store its intermediate results. In the worst case, only one basic algorithm can solve Q in finite time, and all the other basic algorithms run forever without solving Q. To solve Q with a hybrid algorithm constructed from the basic algorithms, we run a basic algorithm for some time, then switch to another, and continue this process until Q is solved. The goal is to solve Q in the least amount of time. Using competitive ratios to measure the efficiency of a hybrid algorithm, we construct an optimal deterministic hybrid algorithm and an efficient randomized hybrid algorithm. This resolves an open question on searching with multiple robots posed by Baeza-Yates, Culberson and Rawlins. We also prove that our randomized algorithm is optimal for λ = 1, settling a conjecture of Kao, Reif and Tate.

Optimal Scheduling of Contract Algorithms for Anytime Problem-Solving

“…This connection was first established by Kao et al (1996Kao et al ( , 1998 in the context of randomized algorithms. The work of Bernstein et al (2003) drew a similar connection between scheduling contract algorithms and robot searching on a set of rays (Alpern & Gal, 2003).…”

“…Clearly, the algorithm must make judicious use of its resources and ensure that it can produce a reasonably good solution, despite having no knowledge of the exact time at which interruptions may occur. As indicated earlier, it is hardly surprising that this setting arises very frequently in the design of AI systems, in applications such as game-playing programs (Althöfer, 1997;Kao, Reif, & Tate, 1996;Kao, Ma, Sipser, & Yin, 1998), e-trading agents, and medical diagnosis systems. Essentially the problem captures a fundamental trade-off between the quality of the solution returned by the algorithm and the amount of available computation time.…”

Scheduling search procedures: The wheel of fortune

“…Online construction of hybrid algorithms for search tasks is stated as another motivation of this line of research in López-Ortiz and Schuierer (2002), following Kao et al (1994).…”

Competitive Search in Symmetric Trees

“…Essentially the same ideas as those used in solving the cow-path problem have been used in the synthesis of deterministic and randomized hybrid algorithms with (near) optimal competitive ratios [2,7]. Given are a number of basic algorithms each of which might (or might not) be useful in solving some problem.…”