Non-Adaptive and Adaptive Two-Sided Search with Fast Objects

TL;DR

This paper analyzes a combinatorial two-sided search model where the searched object can move multiple steps after each test, providing optimal strategies for both adaptive and non-adaptive cases, with surprising equivalence in efficiency.

Contribution

It introduces and analyzes a generalized two-sided search model allowing more moves, and proves the optimality of strategies with an unexpected equivalence between adaptive and non-adaptive approaches.

Findings

Optimal strategies are identified for the generalized model.

Non-adaptive search requires the same number of tests as adaptive search on a path graph.

Strategies can be used for encoding moving object positions in communication channels.

Abstract

In 1946, Koopman introduced a two-sided search model. In this model, a searched object is active and can move, at most, one step after each test. We analyze the model of a combinatorial two-sided search by allowing more moves of the searched object after each test. We give strategies and show that they are optimal. We consider adaptive and non-adaptive strategies. We show the surprising result that with the combinatorial two-sided search on a path graph, the optimal non-adaptive search needs the same number of tests as the corresponding adaptive strategy does. The strategy obtained can also be used as a encoding strategy to sent the position of a moving element through a transmission channel.