The Unbounded Integrality Gap of a Semidefinite Relaxation of the Traveling Salesman Problem

The Unbounded Integrality Gap of a Semidefinite Relaxation of the Traveling Salesman Problem

We study a semidefinite programming relaxation of the traveling salesman problem intro-duced by de Klerk, Pasechnik, and Sotirov [8] and show that their relaxation has an unboundedintegrality gap. In particular, we give a family of instances such that the gap increases linearlywith n. To obtain this result, we search for feasible solutions within a highly structured class of...

the problem of divine hiddenness

این رساله به مساله احتجاب الهی و مشکلات برهان مبتنی بر این مساله میپردازد. مساله احتجاب الهی مساله ای به قدمت ادیان است که به طور خاصی در مورد ادیان ابراهیمی اهمیت پیدا میکند. در ادیان ابراهیمی با توجه به تعالی خداوند و در عین حال خالقیت و حضور او و سخن گفتن و ارتباط شهودی او با بعضی از انسانهای ساکن زمین مساله ای پدید میاید با پرسشهایی از قبیل اینکه چرا ارتباط مستقیم ویا حداقل ارتباط وافی به ب...

Semidefinite Relaxations for the Traveling Salesman Problem

Finding the Exact Integrality Gap for Small Traveling Salesman Problems

The Symmetric Traveling Salesman Problem (STSP) is to find a minimum weight Hamiltonian cycle in a weighted complete graph on n nodes. One direction which seems promising for finding improved solutions for the STSP is the study of a linear relaxation of this problem called the Subtour Elimination Problem (SEP). A well-known conjecture in combinatorial optimization says that the integrality gap ...

On the Integrality Ratio for the Asymmetric Traveling Salesman Problem

We improve the lower bound on the integrality ratio of the Held-Karp bound for asymmetric TSP with triangle inequality from 4/3 to 2. 1. Introduction. The traveling salesman problem (TSP)—the problem of finding a minimum cost tour through a set of cities—is the most celebrated combinatorial optimization problem. It is often used as a testbed for novel ideas, as was the case for Adleman's molecu...