Search-and-Rescue Rendezvous

TL;DR

This paper introduces a new asymmetric rendezvous search problem involving gift transfer or dropping, providing optimal strategies for various scenarios and extending classical rendezvous solutions.

Contribution

It develops optimal agent path and drop-off strategies for gift-based rendezvous problems, expanding on classical models by including gift dropping and transfer options.

Findings

Optimal strategies for gift dropping and transfer identified

Solutions extend classical rendezvous problem to gift-based scenarios

Strategies proven optimal using a rendezvous algorithm

Abstract

We consider a new type of asymmetric rendezvous search problem in which Agent II needs to give Agent I a `gift' which can be in the form of information or material. The gift can either be transfered upon meeting, as in traditional rendezvous, or it can be dropped o? by II at a location he passes, in the hope it will be found by I. The gift might be a water bottle for a traveller lost in the desert; a supply cache for Lieutenant Scott in the Antarctic; or important information (left as a gift). The common aim of the two agents is to minimize the time taken for I to either meet II or find the gift. We find optimal agent paths and droppo? times when the search region is a line, the initial distance between the players is known and one or both of the players can leave gifts. When there are no gifts this is the classical asymmetric rendezvous problem solved by Alpern and Gal in 1995 [10]. We exhibit strategies solving these various problems and use a `rendezvous algorithm' to establish their optimality.