DeepAI

# An Optimal Rounding for Half-Integral Weighted Minimum Strongly Connected Spanning Subgraph

In the weighted minimum strongly connected spanning subgraph (WMSCSS) problem we must purchase a minimum-cost strongly connected spanning subgraph of a digraph. We show that half-integral linear program (LP) solutions for WMSCSS can be efficiently rounded to integral solutions at a multiplicative 1.5 cost. This rounding matches a known 1.5 integrality gap lower bound for a half-integral instance. More generally, we show that LP solutions whose non-zero entries are at least a value f > 0 can be rounded at a multiplicative cost of 2 - f.

• 15 publications
• 6 publications
• 15 publications
08/07/2020

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

Given a connected undirected graph G̅ on n vertices, and non-negative ed...
07/09/2022

### Minimum strongly biconnected spanning directed subgraph problem

Let G=(V,E) be a strongly biconnected directed graph. In this paper we c...
01/05/2018

### Sparse highly connected spanning subgraphs in dense directed graphs

Mader (1985) proved that every strongly k-connected n-vertex digraph con...
11/15/2021

### On a Partition LP Relaxation for Min-Cost 2-Node Connected Spanning Subgraphs

Our motivation is to improve on the best approximation guarantee known f...
05/20/2021

### A (Slightly) Improved Bound on the Integrality Gap of the Subtour LP for TSP

We show that for some ϵ > 10^-36 and any metric TSP instance, the max en...
11/17/2021

### Matroid-Based TSP Rounding for Half-Integral Solutions

We show how to round any half-integral solution to the subtour-eliminati...
11/09/2022

### A 4/3-Approximation Algorithm for Half-Integral Cycle Cut Instances of the TSP

A long-standing conjecture for the traveling salesman problem (TSP) stat...