Related papers: A quasi-polynomial algorithm for well-spaced hyper…
This paper presents a new method for integrated time-optimal routing and trajectory optimization of multirotor unmanned aerial vehicles (UAVs). Our approach extends the well-known Traveling Salesman Problem by accounting for the limited…
This paper implements a new way of solving a problem called the traveling salesman problem (TSP) using quantum genetic algorithm (QGA). We compared how well this new approach works to the traditional method known as a classical genetic…
We develop catalytic algorithms for fundamental problems in algorithm design that run in polynomial time, use only $\mathcal{O}(\log(n))$ workspace, and use sublinear catalytic space matching the best-known space bounds of non-catalytic…
The Metric Traveling Salesman Problem (TSP) is a classical NP-hard optimization problem. The double-tree shortcutting method for Metric TSP yields an exponentially-sized space of TSP tours, each of which approximates the optimal solution…
Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…
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…
This paper ties the line of work on algorithms that find an O(sqrt(log(n)))-approximation to the sparsest cut together with the line of work on algorithms that run in sub-quadratic time by using only single-commodity flows. We present an…
The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem that aims to find the shortest possible route that visits each city exactly once and returns to the starting point. This paper explores the application…
The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, e.g.,…
In the Maximum Independent Set of Objects problem, we are given an $n$-vertex planar graph $G$ and a family $\mathcal{D}$ of $N$ objects, where each object is a connected subgraph of $G$. The task is to find a subfamily $\mathcal{F}…
We give algorithms with running time $2^{O({\sqrt{k}\log{k}})} \cdot n^{O(1)}$ for the following problems. Given an $n$-vertex unit disk graph $G$ and an integer $k$, decide whether $G$ contains (1) a path on exactly/at least $k$ vertices,…
We study approximation algorithms for the following geometric version of the maximum coverage problem: Let P be a set of n weighted points in the plane. We want to place m a * b rectangles such that the sum of the weights of the points in P…
The $k$-Opt algorithm is a local search algorithm for the Traveling Salesman Problem. Starting with an initial tour, it iteratively replaces at most $k$ edges in the tour with the same number of edges to obtain a better tour. Krentel (FOCS…
In the path version of the Travelling Salesman Problem (Path-TSP), a salesman is looking for the shortest Hamiltonian path through a set of n cities. The salesman has to start his journey at a given city s, visit every city exactly once,…
A prominent problem in scheduling theory is the weighted flow time problem on one machine. We are given a machine and a set of jobs, each of them characterized by a processing time, a release time, and a weight. The goal is to find a…
We first show that the Traveling Salesman Problem in an n-vertex graph with average degree bounded by d can be solved in O*(2^{(1-\eps_d)n}) time and exponential space for a constant \eps_d depending only on d, where the O*-notation…
In the Strip Packing problem (SP), we are given a vertical half-strip $[0,W]\times[0,\infty)$ and a set of $n$ axis-aligned rectangles of width at most $W$. The goal is to find a non-overlapping packing of all rectangles into the strip such…
We present a quasi polynomial time approximation scheme (Q-PTAS) for the capacitated vehicle routing problem (CVRP) on $n$ points in the Euclidean plane for arbitrary capacity $c$. The running time is $n^{f(\epsilon)\cdot\log\log n}$ for…
The $k$-opt algorithm is one of the simplest and most widely used heuristics for solving the traveling salesman problem. Starting from an arbitrary tour, the $k$-opt algorithm improves the current tour in each iteration by exchanging up to…
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at…