Fast Partial Distance Estimation and Applications

Abstract

We study approximate distributed solutions to the weighted all-pairs-shortest-paths (APSP) problem in the CONGEST model. We obtain the following results.1. A deterministic (1 + o(1))-approximation to APSP inÕ(n) rounds. This improves over the best previously known algorithm, by both derandomizing it and by reducing the running time by a Θ(log n) factor. In many cases, routing schemes involve relabeling, i.e., assigning new names to nodes and require that these names are used in distance and routing queries. It is known that relabeling is necessary to achieve running times of o(n/ log n). In the relabeling model, we obtain the following results.2. A randomized O(k)-approximation to APSP, for any integer k > 1, running inÕ(n 1/2+1/k + D) rounds, where D is the hop diameter of the network. This algorithm simplifies the best previously known result and reduces its approximation ratio from O(k log k) to O(k). Also, the new algorithm uses uses labels of asymptotically optimal size, namely O(log n) bits. 3. A randomized O(k)-approximation to APSP, for any integer k > 1, running in timeÕ ((nD) 1/2 · n 1/k + D) and producing compact routing tables of sizeÕ(n 1/k ). The node lables consist of O(k log n) bits. This improves on the approximation ratio of Θ(k 2 ) for tables of that size achieved by the best previously known algorithm, which terminates faster, inÕ(n 1/2+1/k + D) rounds.

Distributed exact weighted all-pairs shortest paths in near-linear time

“…The approximate version of the problem was known to admit (i) a (1+o(1))-approximatioñ O(n)-time deterministic algorithm and (ii) anΩ(n) lower bound which holds even against randomizedÕ(poly(n))-approximation algorithms and when D = O(1) [LPS13,LP15,Nan14]. The exact unweighted version was also settled withΘ(n) bound [LP13, HW12, FHW12, PRT12, ACK16].…”

Distributed distance computation and routing with small messages

“…. , t} and all v, w ∈ V i , F connects v and w. Source detection and skeleton spanners have been leveraged in several distributed approximation algorithms for the problem [32][33][34].…”

“…At the heart of any routing protocol lies the computation of short paths between all possible node pairs, which is another This article is based on preliminary results appearing at conferences [32,34,35]. This work has been supported by the Swiss National Science Foundation (SNSF) fundamental challenge that occurs in a multitude of optimization problems.…”

On Efficient Distributed Construction of Near Optimal Routing Schemes

“…From a high level, our approach is similar to those of [LP13a,LP15]. In [LP15], they also use a variant of the TZ-routing scheme, which allows small errors in the distance estimations.…”

“…In [LP15], they also use a variant of the TZ-routing scheme, which allows small errors in the distance estimations. The main difference is in handling the large scales.…”