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There are numerous examples of the so-called ``square root phenomenon'' in the field of parameterized algorithms: many of the most fundamental graph problems, parameterized by some natural parameter $k$, become significantly simpler when…
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…
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 Restricted Shortest Path (RSP) problem, also known as the Delay-Constrained Least-Cost (DCLC) problem, is an NP-hard bicriteria optimization problem on graphs with $n$ vertices and $m$ edges. In a graph where each edge is assigned a…
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,…
Traveling salesman problem is a NP-hard problem. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. Among the existing algorithms, dynamic programming algorithm can solve the problem in time…
The Single-Source Shortest Path (SSSP) problem is well-known for the challenges in developing fast, practical, and work-efficient parallel algorithms. This work introduces a novel shortest path search method. It allows paths with different…
We give a nearly linear time randomized approximation scheme for the Held-Karp bound [Held and Karp, 1970] for metric TSP. Formally, given an undirected edge-weighted graph $G$ on $m$ edges and $\epsilon > 0$, the algorithm outputs in $O(m…
Constant-factor, polynomial-time approximation algorithms are presented for two variations of the traveling salesman problem with time windows. In the first variation, the traveling repairman problem, the goal is to find a tour that visits…
Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…
The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum…
In the Bounded Multiple Traveling Salesman Problem (BMTSP), a tour for each salesman, that starts and ends at the depot and that respects the bounds on the number of cities that a feasible salesman tour should satisfy, is to be constructed.…
The Dubins Traveling Salesman Problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. Currently, there is no algorithm that can find an optimal…
The paper proposes a quantum algorithm for the traveling salesman problem (TSP) based on the Grover Adaptive Search (GAS), which can be successfully executed on IBM's Qiskit library. Under the GAS framework, there are at least two…
This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…
Given a directed graph $G = (V, E)$, the $k$-path partition problem is to find a minimum collection of vertex-disjoint directed paths each of order at most $k$ to cover all the vertices of $V$. The problem has various applications in…
The traveling salesman problem (TSP) famously asks for a shortest tour that a salesperson can take to visit a given set of cities in any order. In this paper, we ask how much faster $k \ge 2$ salespeople can visit the cities if they divide…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…
The Graphical Traveling Salesman Problem with release dates (GTSP-rd) is a variation of the TSP-rd where each vertex in a weighted graph $G$ must be visited at least once, respecting the release date restriction. The edges may be traversed…
We present novel path-slicing strategies integrated with quantum local search to optimize solutions for the Traveling Salesman Problem (TSP), addressing the limitations of current Noisy Intermediate-Scale Quantum (NISQ) technologies. Our…