Multimodal Search on a Line
Jared Coleman, Dmitry Ivanov, Evangelos Kranakis, Danny Krizanc, Oscar, Morales Ponce

TL;DR
This paper introduces a new multimodal linear search problem with unknown target location and mode, providing tight bounds on the competitive ratio and proposing algorithms for optimal and practical search strategies.
Contribution
It establishes the first tight bounds on the competitive ratio for multimodal linear search with unknown target and mode, and develops algorithms for optimal and near-optimal practical search.
Findings
Exact competitive ratios for odd and even number of modes.
Optimal algorithms require infinitesimal movements and infinite direction changes.
Practical approximation algorithms with finite movements and changes.
Abstract
Inspired by the diverse set of technologies used in underground object detection and imaging, we introduce a novel multimodal linear search problem whereby a single searcher starts at the origin and must find a target that can only be detected when the searcher moves through its location using the correct of possible search modes. The target's location, its distance from the origin, and the correct search mode are all initially unknown to the searcher. We prove tight upper and lower bounds on the competitive ratio for this problem. Specifically, we show that when is odd, the optimal competitive ratio is given by , whereas when is even, the optimal competitive ratio is given by : the unique solution to in the interval . This solution has the explicit bounds…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeographic Information Systems Studies
