Abstract
Consider a collection of entities moving continuously with bounded speed, but otherwise unpredictably, in some low-dimensional space. Two such entities encroach upon one another at a fixed time if their separation is less than some specified threshold. Encroachment, of concern in many settings such as collision avoidance, may be unavoidable. However, the associated difficulties are compounded if there is uncertainty about the precise location of entities, giving rise to potential encroachment and, more generally, potential congestion within the full collection.
We consider a model in which entities can be queried for their current location (at some cost) and the uncertainty region associated with an entity grows in proportion to the time since that entity was last queried. The goal is to maintain low potential congestion, measured in terms of the (dynamic) intersection graph of uncertainty regions, at specified (possibly all) times, using the lowest possible query cost. Previous work [SoCG’13, EuroCG’14, SICOMP’16, SODA’19], in the same uncertainty model, addressed the problem of minimizing the congestion potential of point entities using location queries of some bounded frequency. It was shown that it is possible to design query schemes that are O(1)-competitive, in terms of worst-case congestion potential, with other, even clairvoyant query schemes (that exploit knowledge of the trajectories of all entities), subject to the same bound on query frequency.
In this paper we initiate the treatment of a more general problem with the dual optimization objective: minimizing the query frequency, measured as the reciprocal of the minimum time between queries (granularity), while guaranteeing a fixed bound on congestion potential of entities with positive extent at one specified target time. This complementary objective necessitates quite different schemes and analyses. Nevertheless, our results parallel those of the earlier papers, specifically tight competitive bounds on required query frequency.
This work was funded in part by Discovery Grants from the Natural Sciences and Engineering Research Council of Canada.
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Evans, W., Kirkpatrick, D. (2023). Minimizing Query Frequency to Bound Congestion Potential for Moving Entities at a Fixed Target Time. In: Fernau, H., Jansen, K. (eds) Fundamentals of Computation Theory. FCT 2023. Lecture Notes in Computer Science, vol 14292. Springer, Cham. https://doi.org/10.1007/978-3-031-43587-4_12
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DOI: https://doi.org/10.1007/978-3-031-43587-4_12
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