Today I read a paper titled “Optimal Constructions of Hybrid Algorithms”
The abstract is:
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 lambda <= w, we have a computer with lambda 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 lambda = 1, settling a conjecture of Kao, Reif and Tate.