Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, December 12, 2019, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Saeed Ilchi

Multicommodity Routing in Expander Graphs

Given an expander G, a graph with 1/polylog(n) conductance, we want to answer queries of type ``find a path between vertex u and vertex v of G’’. The quality of query responses (a set of paths) is measured by two factors: the maximum length of a path, called dilation, and the maximum number of times that an edge of G appears over all paths, called congestion.

From the work of Leighton and Rao (1999) on multicommodity flows, it is known that if each vertex is asked only in a constant number of queries, there is a set of paths with polylog(n) dilation and polylog(n) congestion. Their algorithm needs to solve LP which is slow for many applications. Ghaffari and Li (2018) improve the running time and propose an almost linear time algorithm by allowing 2^{O(\sqrt{\log n})} dilation and congestion instead of polylog(n). This improves routing messages in a high conductance network which resulted in a framework for simulating algorithms in PRAM model into distributed algorithms (CONGEST model). It can also reconstruct the state of the art result on short cycle decomposition (a recent framework for graph sparsification and sketching).

This talk is based on the work of Mohsen Ghaffari and Jason Li.

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