Related papers: Optimal Longest Paths by Dynamic Programming
We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…
In this paper, we address the numerical solution of the Optimal Transport Problem on undirected weighted graphs, taking the shortest path distance as transport cost. The optimal solution is obtained from the long-time limit of the gradient…
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…
Path finding is a well-studied problem in AI, which is often framed as graph search. Any-angle path finding is a technique that augments the initial graph with additional edges to build shorter paths to the goal. Indeed, optimal algorithms…
In most of the shortest path problems like vehicle routing problems and network routing problems, we only need an efficient path between two points source and destination, and it is not necessary to calculate the shortest path from source…
Here the All-pairs shortest path problem on weighted undirected sparse graphs is being considered. For the problem considered, we propose ``disassembly and assembly of a graph'' algorithm which uses a solution of the problem on a…
In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…
Given a graph $G$, the longest path problem asks to compute a simple path of $G$ with the largest number of vertices. This problem is the most natural optimization version of the well known and well studied Hamiltonian path problem, and…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The…
The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…
Given a graph and a pair of terminals $s$, $t$, the next-to-shortest path problem asks for an $s\!\to \!t$ (simple) path that is shortest among all not shortest $s\!\to \!t$ paths (if one exists). This problem was introduced in 1996, and…
We study an ancient problem that in a static or dynamical system, sought an optimal path, which the context always means within an extremal condition. In fact, through those discussions about this theme, we established a universal essential…
We present the first optimal algorithm for the classical problem of listing all the cycles in an undirected graph. We exploit their properties so that the total cost is the time taken to read the input graph plus the time to list the…
In this paper, we address a class of specially structured problems that include speed planning, for mobile robots and robotic manipulators, and dynamic programming. We develop two new numerical procedures, that apply to the general case and…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…
This paper reviews the overview of the dynamic shortest path routing problem and the various neural networks to solve it. Different shortest path optimization problems can be solved by using various neural networks algorithms. The routing…