Related papers: Query-decision Regression between Shortest Path an…
We introduce a new Steiner-type problem for directed graphs named \textsc{$q$-Root Steiner Tree}. Here one is given a directed graph $G=(V,A)$ and two subsets of its vertices, $R$ of size $q$ and $T$, and the task is to find a minimum size…
We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a ``semi-duality'' between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling…
Various modifications of decision trees have been extensively used during the past years due to their high efficiency and interpretability. Tree node splitting based on relevant feature selection is a key step of decision tree learning, at…
The Minimum Weight Steiner Tree (MST) is an important combinatorial optimization problem over networks that has applications in a wide range of fields. Here we discuss a general technique to translate the imposed global connectivity…
In the Steiner Tree problem we are given an undirected edge-weighted graph as input, along with a set $K$ of vertices called terminals. The task is to output a minimum-weight connected subgraph that spans all the terminals. The famous…
In this paper, we study the problem of finding a minimum weight spanning tree that contains each vertex in a given subset $V_{\rm NT}$ of vertices as an internal vertex. This problem, called Minimum Weight Non-Terminal Spanning Tree,…
We study the use of machine learning techniques to solve a fundamental shortest path problem, known as the single-source many-targets shortest path problem (SSMTSP). Given a directed graph with non-negative edge weights, our goal is to…
Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…
For a metric graph $G=(V,E)$ and $R\subset V$, the internal Steiner minimum tree problem asks for a minimum weight Steiner tree spanning $R$ such that every vertex in $R$ is not a leaf. This note shows a simple polynomial-time…
We consider the minimum spanning tree problem in a setting where the edge weights are stochastic from unknown distributions, and the only available information is a single sample of each edge's weight distribution. In this setting, we…
Finding the shortest path in a graph has applications to a wide range of optimization problems. However, algorithmic methods scale with the size of the graph in terms of time and energy. We propose a method to solve the shortest path…
In this paper we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is…
We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…
Given a weighted, ordered query set $Q$ and a partition of $Q$ into classes, we study the problem of computing a minimum-cost decision tree that, given any query $q$ in $Q$, uses equality tests and less-than comparisons to determine the…
Shortest path queries over graphs are usually considered as isolated tasks, where the goal is to return the shortest path for each individual query. In practice, however, such queries are typically part of a system (e.g., a road network)…
Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently in the presence of some obstacles or constraints. A somewhat related class of problems focuses…
Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
The Steiner tree problem is a well-known problem in network design, routing, and VLSI design. Given a graph, edge costs, and a set of dedicated vertices (terminals), the Steiner tree problem asks to output a sub-graph that connects all…
With applications in distribution systems and communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The…