Unit disk graphs are intersection graphs of circles of unit radius in the plane. We present simple and provably good heuristics for a number of classical NP-hard optimization problems on unit disk graphs. The problems considered include maximum independent set, minimum vertex cover, minimum coloring and minimum dominating set. We also present an on-line coloring heuristic which achieves a compe...

A unit disk graph is the intersection graph of unit disks in the euclidean plane. We present a polynomial-time approximation scheme for the maximum weight independent set problem in unit disk graphs. In contrast to previously known approximation schemes, our approach does not require a geometric representation (specifying the coordinates of the disk centers). The approximation algorithm present...

in this paper we will determine the multiple point manifolds of certain self-transverse immersions in euclidean spaces. following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to dold manifold $v^5$ or a boundary. we will show there is an immersion of $s^7times p^2$ in $mathbb{r}^{13...

Secure set-intersection computation is one of important problems in secure multiparty computation with various applications. We propose a general construction for secure 2-party set-intersection computation based-on anonymous IBE (identity-based encryption) scheme and its user private-keys blind generation techniques. Compared with related works, this construction is provably GUC(generalized un...

Private set operations allow correlation of sensitive data from multiple data owners. Although intensely researched, current solutions still exhibit limited scalability in terms of the supported maximum set size and number of sets. To address these issues, we propose a new approach to private set operations based on a combination of efficient secure multiparty computation and bloom filters, a s...