The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme
نویسندگان
چکیده
منابع مشابه
Polynomial Time Approximation Schemes for the Euclidean Traveling Salesman Problem
In this report, we aim to understand the key ideas and major techniques used in the assigned paper "Polynomial Time Approximation Schemes for Euclidean Traveling Salesman and Other Geometric Problems" by Sanjeev Arora. We also provide a review of related literature with an emphasis on the concurrent work by Joseph S. B. Mitchell. One presentation topic is selected from Arora’s paper and the oth...
متن کاملA Polynomial Time Algorithm for The Traveling Salesman Problem
The ATSP polytope can be expressed by asymmetric polynomial size linear program. Introduction In his seminal work [1], M. Yannakakis proved that the Traveling Salesman problem (TSP) polytope cannot be expressed by symmetric polynomial size linear program, where symmetry means that the polytope is an invariant under vertex relabeling. The question about the size of asymmetric linear programs was...
متن کاملApproximation algorithms for the traveling salesman problem
We first prove that the minimum and maximum traveling salesman problems, their metric versions as well as some versions defined on parameterized triangle inequalities (called sharpened and relaxed metric traveling salesman) are all equi-approximable under an approximation measure, called differential-approximation ratio, that measures how the value of an approximate solution is placed in the in...
متن کاملA Fully Polynomial Time Approximation Scheme for Packing While Traveling
Understanding the interactions between different combinatorial optimisation problems in real-world applications is a challenging task. Recently, the traveling thief problem (TTP), as a combination of the classical traveling salesperson problem and the knapsack problem, has been introduced to study these interactions in a systematic way. We investigate the underlying non-linear packing while tra...
متن کاملA polynomial time approximation scheme for the MRCT problem∗
The ratio achieves its minimum when the two terms coincide, i.e., δ = 1/4, and the minimum ratio is 4/3. In fact, by using a general star and a (1/4)-separator, it is possible to approximate an MRCT with ratio (4/3) + ε for any constant ε > 0 in polynomial time. The additional error ε is due to the difference between the guessed and the true separators. By this strategy, the approximation ratio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2016
ISSN: 0097-5397,1095-7111
DOI: 10.1137/130913328