Invariant Matching

PIMS-MPrime Summer School in Probability

授课人:Alexander Holroyd

机构:Pacific Institute for the Mathematical Sciences(PIMS)

关键词: Scientific;    Mathematics;    Probability;    Invariant Matching;   

加拿大|英语

【 摘 要 】

Suppose that red and blue points occur as independent point processes in Rd, and consider translation-invariant schemes for perfectly matching the red points to the blue points. (Translation-invariance can be interpreted as meaning that the matching is constructed in a way that does not favour one spatial location over another). What is best possible cost of such a matching, measured in terms of the edge lengths? What happens if we insist that the matching is non-randomized, or if we forbid edge crossings, or if the points act as selfish agents? I will review recent progress and open problems on this topic, as well as on the related topic of fair allocation. In particular I will address some surprising new discoveries on multi-colour matching and multi-edge matching.

【 授权许可】

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