Fast Approximations for Metric-TSP via Linear Programming

Approximation Algorithms for Path TSP, ATSP, and TAP via Relaxations

Linear programming (LP) relaxations provide a powerful technique to design approximation algorithms for combinatorial optimization problems. In the first part of the thesis, we study the metric s-t path Traveling Salesman Problem (TSP) via LP relaxations. We first consider the s-t path graph-TSP, a critical special case of the metric s-t path TSP. We design a new simple LP-based algorithm for t...

TSP on Cubic and Subcubic Graphs

We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NP-hard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says that the integrality gap, i.e., the worst case ratio between the optimal values of the TSP and its linear programming relaxation, is 4/3. Using polyhedral tec...

Improved and Derandomized Approximations for Two-Criteria Metric Traveling Salesman

We improve and derandomize the best known approximation algorithm for the twocriteria metric traveling salesman problem (2-TSP). More precisely, we construct a deterministic 2-approximation which answers an open question by Manthey. Moreover, we show that 2-TSP is randomized (3/2 + ε, 2)-approximable, and we give the first randomized approximations for the two-criteria traveling salesman path p...

Double-Tree Approximations for Metric TSP: Is the Best One Good Enough?

The traveling salesman problem on cubic and subcubic graphs

We study the Travelling Salesman Problem (TSP) on the metric completion of cubic and subcubic graphs, which is known to be NPhard. The problem is of interest because of its relation to the famous 4/3 conjecture for metric TSP, which says that the integrality gap, i.e., the worst case ratio between the optimal values of the TSP and its linear programming relaxation (the subtour elimination relax...