Related papers: A DP Approach to Hamiltonian Path Problem
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel shared memory computer. Our robust path tracker applies Newton's method on power series to locate the closest singular parameter value. On…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
In this paper we introduce the notion of a complete time graph of order n. We define time paths and Hamiltonian time paths in a complete time graph. Each Hamiltonian time path (htp) is associated with some permutation p of the integers 1 to…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
Distributing computations among agents in large networks reduces computational effort in multi-agent path finding (MAPF). One distribution strategy is prioritized planning (PP). In PP, we couple and prioritize interacting agents to achieve…
A polynomial time algorithm which detects all paths and cycles of all lengths in form of vertex pairs (start, finish).
We present an algorithm to solve a system of diagonal polynomial equations over finite fields when the number of variables is greater than some fixed polynomial of the number of equations whose degree depends only on the degree of the…
The famous Chinese Postman Problem (CPP) is polynomial time solvable on both undirected and directed graphs. Gutin et al. [Discrete Applied Math 217 (2016)] generalized these results by proving that CPP on $c$-edge-colored graphs is…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…
We introduce an iterative method to search for time-optimal Hamiltonians that drive a quantum system between two arbitrary, and in general mixed, quantum states. The method is based on the idea of progressively improving the efficiency of…
In this paper we present an algorithm for finding a minimum dominator coloring of orientations of paths. To date this is the first algorithm for dominator colorings of digraphs in any capacity. We prove that the algorithm always provides a…
We present a gradient-based identification algorithm to identify the system matrices of a linear port-Hamiltonian system from given input-output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal…
We study the generalized minimum Manhattan network (GMMN) problem: given a set $P$ of pairs of two points in the Euclidean plane $\mathbb{R}^2$, we are required to find a minimum-length geometric network which consists of axis-aligned…
The max-cut problem is a classical graph theory problem which is NP-complete. The best polynomial time approximation scheme relies on \emph{semidefinite programming} (SDP). We study the conditions under which graphs of certain classes have…
We study three classical graph problems - Hamiltonian path, minimum spanning tree, and minimum perfect matching on geometric graphs induced by bichromatic (red and blue) points. These problems have been widely studied for points in the…
Many complex questions in biology, physics, and mathematics can be mapped to the graph isomorphism problem and the closely related graph automorphism problem. In particular, these problems appear in the context of network visualization,…
The problem of high-dimensional path-dependent optimal stopping (OS) is important to multiple academic communities and applications. Modern OS tasks often have a large number of decision epochs, and complicated non-Markovian dynamics,…
Adleman showed that deoxyribonucleic acid DNA strands could be employed towards calculating solutions to an instance of the Hamiltonian path problem . Lipton also demonstrated that Adleman techniques could be used to solve the…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
We prove two dichotomy results for detecting long paths as patterns in a given graph. The NP-hard problem Longest Induced Path is to determine the longest induced path in a graph. The NP-hard problem Longest Path Contractibility is to…