Shortest $$(A+B)$$-Path Packing Via Hafnian

Shortest (A+B)-path packing via hafnian

Björklund and Husfeldt developed a randomized polynomial time algorithm to solve the shortest two disjoint paths problem. Their algorithm is based on computation of permanents modulo 4 and the isolation lemma. In this paper, we consider the following generalization of the shortest two disjoint paths problem, and develop a similar algebraic algorithm. The shortest perfect (A + B)-path packing pr...

Secluded Path via Shortest Path

We provide several new algorithmic results for the secluded path problem, specifically approximation and optimality results for the static algorithm of [3, 5], and an extension (h-Memory) of it based on de Bruijn graphs, when applied to bounded degree graphs and some other special graph classes which can model wireless communication and line-of-sight settings. Our primary result is that h-Memor...

Ultrafast Shortest-Path Queries via Transit Nodes

Metric Embedding via Shortest Path Decompositions

We study the problem of embedding weighted graphs of pathwidth k into `p spaces. Our main result is an O(kmin{/p,/2})-distortion embedding. For p = 1, this is a super-exponential improvement over the best previous bound of Lee and Sidiropoulos. Our distortion bound is asymptotically tight for any fixed p > 1. Our result is obtained via a novel embedding technique that is based on low depth deco...

Faster Distributed Shortest Path Approximations via Shortcuts

A long series of recent results and breakthroughs have led to faster and better distributed approximation algorithms for single source shortest paths (SSSP) and related problems in the CONGEST model. The runtime of all these algorithms, however, is Ω̃( √ n), regardless of the network topology, even on nice networks with a (poly)logarithmic network diameter D. While this is known to be necessary ...