We consider the problem of partitioning the set of vertices of a given unit
disk graph (UDG) into a minimum number of cliques. The problem is NP-hard and
various constant factor approximations are known, with the current best ratio
of 3. Our main result is a {\em weakly robust} polynomial time approximation
scheme (PTAS) for UDGs expressed with edge-lengths, it either (i) computes a
clique partition or (ii) gives a certificate that the graph is not a UDG; for
the case (i) that it computes a clique partition, we show that it is guaranteed
to be within (1+\eps) ratio of the optimum if the input is UDG; however if
the input is not a UDG it either computes a clique partition as in case (i)
with no guarantee on the quality of the clique partition or detects that it is
not a UDG. Noting that recognition of UDG's is NP-hard even if we are given
edge lengths, our PTAS is a weakly-robust algorithm. Our algorithm can be
transformed into an O(\frac{\log^* n}{\eps^{O(1)}}) time distributed PTAS.
We consider a weighted version of the clique partition problem on vertex
weighted UDGs that generalizes the problem. We note some key distinctions with
the unweighted version, where ideas useful in obtaining a PTAS breakdown. Yet,
surprisingly, it admits a (2+\eps)-approximation algorithm for the weighted
case where the graph is expressed, say, as an adjacency matrix. This improves
on the best known 8-approximation for the {\em unweighted} case for UDGs
expressed in standard form.Comment: 21 pages, 9 figure