Optimal Constructions of Hybrid Algorithms

Title: Optimal Constructions of Hybrid Algorithms

Abstract: This research article explores the efficiency of on-line strategies for solving problems with hybrid algorithms. It focuses on a scenario where there is a problem Q and multiple basic algorithms for solving Q. The algorithms are run on a computer with multiple memory areas, and the goal is to solve Q in the least amount of time. The study uses competitive ratios to measure the efficiency of a hybrid algorithm.

Main Research Question: How can we construct the most efficient deterministic and randomized hybrid algorithms for solving problems with multiple basic algorithms?

Methodology: The research proposes an optimal deterministic hybrid algorithm and an efficient randomized hybrid algorithm. It uses competitive ratios to compare the efficiency of these algorithms.

Results: The study resolves an open question on searching with multiple robots posed by Baeza-Yates, Culberson, and Rawlins. It also proves that the randomized algorithm is optimal for λ= 1, settling a conjecture of Kao, Reif, and Tate.

Implications: The research has implications for the field of computer science, particularly in the areas of online algorithms and robotics. It provides insights into the optimal way to solve problems with multiple basic algorithms and multiple robots. The study also contributes to the understanding of competitive ratios and their application in measuring the efficiency of algorithms.

Link to Article: https://arxiv.org/abs/0101028v1 Authors: arXiv ID: 0101028v1