Maximum Length-Constrained Flows and Disjoint Paths: Distributed, Deterministic, and Fast
PROCEEDINGS OF THE 55TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING, STOC 2023(2023)
摘要
Computing routing schemes that support both high throughput and low latency is one of the core challenges of network optimization. Such routes can be formalized as h-length flows which are defined as flows whose flow paths have length at most h. Many well-studied algorithmic primitives-such as maximal and maximum length-constrained disjoint paths-are special cases of h-length flows. Likewise the optimal h-length flow is a fundamental quantity in network optimization, characterizing, up to poly-log factors, how quickly a network can accomplish numerous distributed primitives. In this work, we give the first efficient algorithms for computing (1 - epsilon)-approximate h-length flows that are nearly "as integral as possible." We give deterministic algorithms that take (O) over tilde (poly(h, 1/epsilon)) parallel time and (O) over tilde (poly(h, 1/epsilon) center dot 2(O) (root log n)) distributed CONGEST time. We also give a CONGEST algorithm that succeeds with high probability and only takes (O) over tilde (poly(h, 1/epsilon)) time. Using our h-length flow algorithms, we give the first efficient deterministic CONGEST algorithms for the maximal disjoint paths problem with length constraints-settling an open question of Chang and Saranurak (FOCS 2020)-as well as essentially-optimal parallel and distributed approximation algorithms for maximum length-constrained disjoint paths. The former greatly simplifies deterministic CONGEST algorithms for computing expander decompositions. We also use our techniques to give the first efficient and deterministic (1-epsilon)-approximation algorithms for bipartite b-matching in CONGEST. Lastly, using our flow algorithms, we give the first algorithms to efficiently compute h-length cutmatches, an object at the heart of recent advances in length-constrained expander decompositions.
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关键词
length-bounded flows,hop-bounded flows,distributed algorithms,parallel algorithms,flow rounding,cycle covers,b-matching
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