A Space-Constrained Interval Selection

In this paper we consider the interval selection problem, namely, finding a maximum cardinality subset of disjoint intervals from a given collection of intervals on the real line. A celebrated algorithm of Gavril [17] that picks the intervals greedily in increasing order of their right endpoint yields an optimal solution in the classic setting where the complete set of intervals is known to the algorithm. Here we study this problem in the streaming model [19; 26], where the input is given to the algorithm as a stream of items (intervals in our case), one at a time, and the algorithm has a limited memory that precludes storing the whole input. Yet, the algorithm is still required to output a feasible solution, with a good approximation ratio. The motivation for the streaming model stems, inter alia, from applications of managing very large data sets, such as biological data, (cf. [24]), network traffic data, (cf. [28]), and more. Although some function of the whole data set is to be computed, it is impossible to store the whole input. Depending on the setting, different variants of the streaming model have been considered in the literature, such as the classical