AI Chat AI Image Generator AI Video Text to Speech

Short Combinatorial Proof that the DFJ Polytope is contained in the MTZ Polytope for the Asymmetric Traveling Salesman Problem

05/17/2018

∙

by Mark Velednitsky, et al.

∙

∙

For the Asymmetric Traveling Salesman Problem (ATSP), it is known that the Dantzig-Fulkerson-Johnson (DFJ) polytope is contained in the Miller-Tucker-Zemlin (MTZ) polytope. The analytic proofs of this fact are quite long. Here, we present a proof which is combinatorial and significantly shorter by relating the formulation to distances in a modified graph.

page 1

page 2

research

∙ 10/11/2019

A Proof of Levi's Extension Lemma

We give a short and self-contained proof of Levi's Extension Lemma for p...

0 Marcus Schaefer, et al. ∙

research

∙ 07/02/2019

A Short Proof of the Toughness of Delaunay Triangulations

We present a self-contained short proof of the seminal result of Dillenc...

0 Ahmad Biniaz, et al. ∙

research

∙ 08/10/2021

Tutorial on the Robust Interior Point Method

We give a short, self-contained proof of the interior point method and i...

0 Yin Tat Lee, et al. ∙

research

∙ 12/16/2022

Antichain Codes

A family of sets A is said to be an antichain if x⊄y for all distinct x,...

0 Benjamin Gunby, et al. ∙

research

∙ 12/25/2022

Simple proof of the risk bound for denoising by exponential weights for asymmetric noise distributions

In this note, we consider the problem of aggregation of estimators in or...

0 Arnak S. Dalalyan, et al. ∙

research

∙ 03/01/2023

A linear bound for the Colin de Verdière parameter μ for graphs embedded on surfaces

We provide a combinatorial and self-contained proof that for all graphs ...

0 Camille Lanuel, et al. ∙

research

∙ 08/20/2020

A Simple Proof of Optimal Approximations

The fundamental result of Li, Long, and Srinivasan on approximations of ...

0 Monika Csikos, et al. ∙