Abstract
We consider the problem of exploring and triangulating a region with a swarm of robots with limited vision and communication range. For an unknown polygonal region P, the Online Minimum Relay Triangulation Problem (OMRTP) asks for an exploration strategy that maintains a triangulation with limited edge length and achieves a minimum number of robots (relays), such that the triangulation covers P; for a given number n of robots, the Online Maximum Area Triangulation Problem (OMATP) asks for maximizing the triangulated area. Both problems have been studied before, with a competitive factor of 3 for the OMRTP in general polygons, and an unbounded competitive factor for the OMATP; the latter holds for polygons with very narrow corridors.
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