Online unit covering in L_2
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Given a set of points P in L_2, the classic Unit Covering (UC) problem asks to compute the minimum number of unit disks (possibly intersecting) required to cover the points in P, along with a placement of the disks. In this paper, we study an online version of UC in L_2, which we call as Online Unit Covering (OUC) in L_2, or, simply Online Unit Covering (OUC). In OUC, the points arrive online sequentially. Once a point p arrives, a decision needs to be taken - either assign p to a previously placed disk (if possible) or place a new disk to cover p since none of the previously placed disks can cover p. In this setup, once a disk is placed, its placement cannot be altered in future. We show that competitive ratio of an optimal deterministic online algorithm for OUC is at least 3 and at most 5.
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