The line-of-sight networks is a network model introduced recently by Frieze et al. (SODA’07). It considers scenarios of wireless networks in which the underlying environment has a large number of obstacles and the communication can only take place between objects that are close in space and are in the line of sight (are visible) to one another. To capture the main properties of this model, Frie...

We discover a surprising connection between graph coloring in two orthogonal paradigms: parallel and on-line computing. We present a randomized on-line coloring algorithm with a performance ratio of O(n= log n), an improvement of p log n factor over the previous best known algorithm of Vishwanathan. Also, from the same principles, we construct a parallel coloring algorithm with the same perform...

This paper investigates, how two fundamental measurement operations in Euclidean space, namely the construction of a straight line of given orientation angle and the measurement of distances along this line, are mapped to the non-Euclidean log-polar image plane. It is shown, how these two operations can be efficiently implemented for discrete log-polar images. The measurement operations are use...

We present output-sensitive scalable parallel algorithms for bichromatic line segment intersection problems for the coarse grained multicomputer model. Under the assumption that n p 2 , where n is the number of line segments and p the number of processors, we obtain an intersection counting algorithm with a time complexity of O(n log n log p p + T s (n log p; p)), where T s (m; p) is the time u...

Given a simple polygon P in the plane, we present new algorithms and data structures for computing the weak visibility polygon from any query line segment in P . We build a data structure in O(n) time and O(n) space that can compute the visibility polygon for any query line segment s in O(k log n) time, where k is the size of the visibility polygon of s and n is the number of vertices of P . Al...

We present a deterministic algorithm running in space O ? log 2 n= log logn solving the connectivity problem on strongly unambiguous graphs. In addition, we present an O(logn) time-bounded algorithm for this problem running on a parallel pointer machine.