Related papers: Recognising permuted Demidenko matrices
TSP (Traveling Salesman Problem), a classic NP-complete problem in combinatorial optimization, is of great significance in multiple fields. Exact algorithms for TSP are not practical due to their exponential time cost. Thus, approximate…
This paper is example 5 in chapter 5. Let H be an n-cycle. A permutation s is H-admissible if Hs = H' where H' is an n-cycle. Here we define a 19 X 19 matrix, M, in the following way: We obtain the remainders modulo 100 of each of the…
The moving target traveling salesman problem with obstacles (MT-TSP-O) is a generalization of the traveling salesman problem (TSP) where, as its name suggests, the targets are moving. A solution to the MT-TSP-O is a trajectory that visits…
The Traveling Salesman Problem (TSP) is a prototypical combinatorial optimization problem, but its quantum implementation is limited by the O(n^2)-qubit overhead of standard one-hot encodings. Here, we propose a resource-efficient…
This work presents a tensor-network formulation of the Traveling Salesman Problem (TSP) and several of its variants. The approach represents candidate tours with tensor-network layers, weights them by Boltzmann factors, and enforces…
An important variant of the classic Traveling Salesman Problem (TSP) is the Dynamic TSP, in which a system with dynamic constraints is tasked with visiting a set of n target locations (in any order) in the shortest amount of time. Such…
The traveling-salesman problem is one of the most studied combinatorial optimization problems, because of the simplicity in its statement and the difficulty in its solution. We study the traveling salesman problem when the positions of the…
This paper presents a method for calculating Region of Attraction of a target set (not necessarily an equilibrium) for controlled polynomial dynamical systems, using a hierarchy of semidefinite programming problems (SDPs). Our approach…
In this paper, we consider the problem of representing a multivariate polynomial as the determinant of a definite (monic) symmetric/Hermitian linear matrix polynomial (LMP). Such a polynomial is known as determinantal polynomial.…
Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods. However, when the dimension of the problem gets large, interior point methods become impractical in terms of both computational time and memory…
Various neural network models have been proposed to tackle combinatorial optimization problems such as the travelling salesman problem (TSP). Existing learning-based TSP methods adopt a simple setting that the training and testing data are…
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…
Traveling Salesman Problem (TSP) is a classic NP-hard problem that has garnered significant attention from both academia and industry. While neural-based methods have shown promise for solving TSPs, they still face challenges in scaling to…
This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once…
Reinforcement learning has recently shown promise in learning quality solutions in many combinatorial optimization problems. In particular, the attention-based encoder-decoder models show high effectiveness on various routing problems,…
We consider the {\em Shaped Partition Problem} of partitioning $n$ given vectors in real $k$-space into $p$ parts so as to maximize an arbitrary objective function which is convex on the sum of vectors in each part, subject to arbitrary…
We show that the Identity Problem is decidable in polynomial time for finitely generated sub-semigroups of the group $\mathsf{UT}(4, \mathbb{Z})$ of $4 \times 4$ unitriangular integer matrices. As a byproduct of our proof, we also show the…
We introduce the Polychromatic Traveling Salesman Problem (PCTSP), where the input is an edge weighted graph whose vertices are partitioned into $k$ equal-sized color classes, and the goal is to find a minimum-length Hamiltonian cycle that…
We provide a new upper bound for traveling salesman problem (TSP) in cubic graphs, i.e. graphs with maximum vertex degree three, and prove that the problem for an $n$-vertex graph can be solved in $O(1.2553^n)$ time and in linear space. We…
The Multiple Depot Ring-Star Problem (MDRSP) is an important combinatorial optimization problem that arises in the context of optical fiber network design, and in applications pertaining to collecting data using stationary sensing devices…