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| Content Provider | ACM Digital Library |
|---|---|
| Author | Yaroslavtsev, Grigory Li, Yang Assadi, Sepelir Khanna, Sanjeev |
| Abstract | We study the problem of finding an approximate maximum matching in two closely related computational models, namely, the dynamic graph streaming model and the simultaneous multi-party communication model. In the dynamic graph streaming model, the input graph is revealed as a stream of edge insertions and deletions, and the goal is to design a small space algorithm to approximate the maximum matching. In the simultaneous model, the input graph is partitioned across k players, and the goal is to design a protocol where the k players simultaneously send a small-size message to a coordinator, and the coordinator computes an approximate matching. Dynamic graph streams. We resolve the space complexity of single-pass turnstile streaming algorithms for approximating matchings by showing that for any ε > 0, $Θ(n^{2-3ε})$ space is both sufficient and necessary (up to polylogarithmic factors) to compute an $n^{ε}-approximate$ matching; here n denotes the number of vertices in the input graph. The simultaneous communication model. Our results for dynamic graph streams also resolve the (per-player) simultaneous communication complexity for approximating matchings in the edge partition model. For the vertex partition model, we design new randomized and deterministic protocols for k players to achieve an α-approximation. Specifically, for α ≥ [EQUATION], we provide a randomized protocol with total communication of $O(nk/α^{2})$ and a deterministic protocol with total communication of O(nk/α). Both these bounds are tight. Our work generalizes the results established by Dobzinski et al. (STOC 2014) for the special case of k = n. Finally, for the case of α = o([EQUATION]), we establish a new lower bound on the simultaneous communication complexity which is super-linear in n. |
| Starting Page | 1345 |
| Ending Page | 1364 |
| Page Count | 20 |
| File Format | |
| ISBN | 9781611974331 |
| Language | English |
| Publisher | Association for Computing Machinery (ACM) |
| Publisher Date | 2016-01-10 |
| Access Restriction | Subscribed |
| Content Type | Text |
| Resource Type | Article |
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