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Combinatorial Optimization Reading Group - Sharat IbrahimpurExport this event to calendar

Friday, July 24, 2020 — 1:30 PM EDT

Title: A 4/3-Approximation Algorithm for the Minimum 2-Edge Connected Multisubgraph Problem in the Half-Integral Case

Speaker: Sharat Ibrahimpur
Affiliation: University of Waterloo
Zoom: Contact Sharat Ibrahimpur

Abstract:

Given a connected undirected graph G on n vertices, and non-negative edge costs c, the 2ECM problem is that of finding a 2-edge connected spanning multisubgraph of G of minimum cost. The natural linear program (LP) for 2ECM, which coincides with the subtour LP for the Traveling Salesman Problem on the metric closure of G, gives a lower bound on the optimal cost. For instances where this LP is optimized by a half-integral solution x, Carr and Ravi (1998) showed that the integrality gap is at most 4/3: they show that the vector 4x/3 dominates a convex combination of incidence vectors of 2-edge connected spanning multisubgraphs of G.

We present a simpler proof of the result due to Carr and Ravi by applying an extension of Lovasz's splitting-off theorem. Our proof naturally leads to a 4/3-approximation algorithm for half-integral instances. Given a half-integral solution x to the 2ECM LP, we give an O(n^2)-time algorithm to obtain a 2-edge connected spanning multisubgraph of G whose cost is at most 4/3 c^T x.

This is joint work with Sylvia Boyd, Joseph Cheriyan, Robert Cummings, Logan Grout, Zoltan Szigeti, and Lu Wang.

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