Parallel interval order recognition and construction of interval representations

Parallel Interval Order Recognition and Construction of Interval Representations

Parallel algorithms for recognizing and representing interval orders are proposed for differ. ent models of parallel random access machines (PRAM). The algorithms accept as input a transitively~losed directed graph with N nodes and M edges. They run in time O0og N) with O(N + M~ processors and O{N + M} space and in co , tam time with O(N z) proces~rs and O{N ~) space depending on the data struc...

Bounded Representations of Interval and Proper Interval Graphs

Klav́ık et al. [arXiv:1207.6960] recently introduced a generalization of recognition called the bounded representation problem which we study for the classes of interval and proper interval graphs. The input gives a graph G and in addition for each vertex v two intervals Lv and Rv called bounds. We ask whether there exists a bounded representation in which each interval Iv has its left endpoint ...

Weak Representations of Interval Algebras

Ladkin and Maddux [LaMa87] showed how to interpret the calculus of time intervals defined by Allen [AZ2831 in terms of representations of a particular relation algebra, and proved that this algebra has a unique countable representation up to isomorphism. In this paper, we . consider the algebra An of n-intervals, which coincides with Allen’s algebra for n=2, and prove that An has a unique count...

Fast and Parallel Interval Arithmetic

Parallel Detection of Interval Overlapping

In this paper we define the interval overlapping relation and develop a parallel hardware unit for its realization. As one application we consider the interval comparisons. It is shown that a detailed classification of the interval overlapping relation leads to a reduction of floatingpoint comparisons in common applications.