Related papers: Dijkstra meets Steiner: a fast exact goal-oriented…
All traditional methods of computing shortest paths depend upon edge-relaxation where the cost of reaching a vertex from a source vertex is possibly decreased if that edge is used. We introduce a method which maintains lower bounds as well…
We propose an optimal algorithm for solving the longest path problem in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster than other state-of-the-art…
This paper addresses a graph optimization problem, called the Witness Tree problem, which seeks a spanning tree of a graph minimizing a certain non-linear objective function. This problem is of interest because it plays a crucial role in…
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…
We propose polynomial-time algorithms that sparsify planar and bounded-genus graphs while preserving optimal or near-optimal solutions to Steiner problems. Our main contribution is a polynomial-time algorithm that, given an unweighted graph…
Recent years have witnessed rapid advances in the use of neural networks to solve combinatorial optimization problems. Nevertheless, designing the "right" neural model that can effectively handle a given optimization problem can be…
The goal for the Directed Steiner Tree problem is to find a minimum cost tree in a directed graph G=(V,E) that connects all terminals X to a given root r. It is well known that modulo a logarithmic factor it suffices to consider acyclic…
We study connectivity problems from a fine-grained parameterized perspective. Cygan et al. (TALG 2022) obtained algorithms with single-exponential running time $\alpha^{tw} n^{O(1)}$ for connectivity problems parameterized by treewidth…
Suppose a target is hidden in one of the vertices of an edge-weighted graph according to a known probability distribution. The expanding search problem asks for a search sequence of the vertices so as to minimize the expected time for…
Using Dijkstra's algorithm to compute the shortest paths in a graph from a single source node to all other nodes is common practice in industry and academia. Although the original description of the algorithm advises using a Fibonacci Heap…
Finding spanning trees under various constraints is a classic problem with applications in many fields. Recently, a novel notion of "dense" ("sparse") tree, and in particular spanning tree (DST and SST respectively), is introduced as the…
We present an algorithm for a fault tolerant Depth First Search (DFS) Tree in an undirected graph. This algorithm is drastically simpler than the current state-of-the-art algorithms for this problem, uses optimal space and optimal…
Generic Dijkstra is a novel algorithm for finding the optimal shortest path in both wavelength-division multiplexed networks (WDM) and elastic optical networks (EON), claimed to outperform known algorithms considerably. Because of its…
Given a graph $G = (V,E)$ and a subset $T \subseteq V$ of terminals, a \emph{Steiner tree} of $G$ is a tree that spans $T$. In the vertex-weighted Steiner tree (VST) problem, each vertex is assigned a non-negative weight, and the goal is to…
The 1-Steiner tree problem, the problem of constructing a Steiner minimum tree containing at most one Steiner point, has been solved in the Euclidean plane by Georgakopoulos and Papadimitriou using plane subdivisions called oriented…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
We present a novel algorithm for dynamic routing with dedicated path protection which, as the presented simulation results suggest, can be efficient and exact. We present the algorithm in the setting of optical networks, but it should be…
Short spanning trees subject to additional constraints are important building blocks in various approximation algorithms. Especially in the context of the Traveling Salesman Problem (TSP), new techniques for finding spanning trees with…
In this paper, we consider the Uniform Cost-Distance Steiner Tree Problem in metric spaces, a generalization of the well-known Steiner tree problem. Cost-distance Steiner trees minimize the sum of the total length and the weighted path…
Cartesian tree matching is the problem of finding all substrings of a given text which have the same Cartesian trees as that of a given pattern. So far there is one linear-time solution for Cartesian tree matching, which is based on the KMP…