Problem
Research questions and friction points this paper is trying to address.
communication complexity
maximum matching
negative-weight shortest paths
graph problems
two-party communication
On the Communication Complexity of Maximum Matching and Negative-Weight Shortest Paths
🤖 AI Summary
This work investigates the communication complexity of fundamental graph problems in the deterministic two-party communication model, with a focus on maximum matching and single-source shortest paths with negative weights (including negative cycle detection). For both general and bipartite graphs, the paper introduces novel and streamlined communication protocols that eschew traditional, intricate reductions. Instead, the approach integrates vertex potentials, discretization arguments, and combinatorial optimization techniques. The main contributions include a protocol for maximum matching in general graphs with communication complexity $\tilde{O}(n^{3/2})$, and protocols requiring only $\tilde{O}(n)$ bits of communication for both negative-weight single-source shortest paths and maximum matching in bipartite graphs—substantially simplifying and improving upon existing methods.
📝 Abstract
We revisit several fundamental graph problems in the deterministic two-party communication model. Our main contributions include: (1) a new $\widetilde{O}(n^{3/2})$-bit protocol for computing a maximum matching in general graphs. While the same upper bound can be obtained by simulating the classic algorithms of Micali-Vazirani and Gabow, our protocol is conceptually simple and avoids the intricacies of finding a maximal set of shortest augmenting paths; (2) a new $\widetilde{O}(n)$-bit protocol for negative-cycle detection and negative-weight single-source shortest paths. Our protocol simplifies that of Blikstad et al. by replacing a long chain of reductions with a more direct approach based on vertex potentials; (3) a combinatorial $\widetilde{O}(n)$-bit protocol for computing a maximum matching in bipartite graphs, obtained by reinterpreting the near-linear communication protocol of Blikstad et al. through a discretized analysis. Together, these results provide simpler protocols for several basic graph problems. We hope they will inspire further advances on the communication complexity of a wide range of graph problems.
Innovation
Methods, ideas, or system contributions that make the work stand out.
communication complexity
maximum matching
negative-weight shortest paths
vertex potentials
combinatorial protocol
🔎 Similar Papers
No similar papers found.
💼 Related Jobs
