Space-Constrained Interval Selection

Details Space-Constrained Interval Selection Space-Constrained Interval Selection

2012-02-20

arxiv.org/abs/1202.4326v1

Computer Science

Data Structures and Algorithms

Scientific paper

We study streaming algorithms for the interval selection problem: finding a maximum cardinality subset of disjoint intervals on the line. A deterministic 2-approximation streaming algorithm for this problem is developed, together with an algorithm for the special case of proper intervals, achieving improved approximation ratio of 3/2. We complement these upper bounds by proving that they are essentially best possible in the streaming setting: it is shown that an approximation ratio of $2 - \epsilon$ (or $3 / 2 - \epsilon$ for proper intervals) cannot be achieved unless the space is linear in the input size. In passing, we also answer an open question of Adler and Azar \cite{AdlerAzar03} regarding the space complexity of constant-competitive randomized preemptive online algorithms for the same problem.

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