Semi-Streaming Algorithms for Weighted k-Disjoint Matchings

We design and implement two single-pass semi-streaming algorithms for the maximum weight k-disjoint matching (k-DM) problem. Given an integer k, the k-DM problem is to find k pairwise edge-disjoint matchings such that the sum of the weights of the matchings is maximized. For k ≥ 2, this problem is NP-hard. Our first algorithm is based on the primal-dual framework of a linear programming relaxation of the problem and is 1/3+ε-approximate. We also develop an approximation preserving reduction from k-DM to the maximum weight b-matching problem. Leveraging this reduction and an existing semi-streaming b-matching algorithm, we design a (1/2+ε)(1 - 1/k+1)-approximate semi-streaming algorithm for k-DM. For any constant ε > 0, both of these algorithms require O(nk log_1+ε^2 n) bits of space. To the best of our knowledge, this is the first study of semi-streaming algorithms for the k-DM problem. We compare our two algorithms to state-of-the-art offline algorithms on 95 real-world and synthetic test problems, including thirteen graphs generated from data center network traces. On these instances, our streaming algorithms used significantly less memory (ranging from 6× to 512× less) and were faster in runtime than the offline algorithms. Our solutions were often within 5 the existing offline algorithms run out of 1 TB memory for most of the large instances (>1 billion edges), whereas our streaming algorithms can solve these problems using only 100 GB memory for k=8.