Related papers: Special Cases of the Minimum Spanning Tree Problem…
A minimum dominating set in a graph is a minimum set of vertices such that every vertex of the graph either belongs to it, or is adjacent to one vertex of this set. This mathematical object is of high relevance in a number of applications…
We consider the stochastic geometry model where the location of each node is a random point in a given metric space, or the existence of each node is uncertain. We study the problems of computing the expected lengths of several…
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…
Using Machine Learning systems in the real world can often be problematic, with inexplicable black-box models, the assumed certainty of imperfect measurements, or providing a single classification instead of a probability distribution. This…
We survey $k$-best enumeration problems and the algorithms for solving them, including in particular the problems of finding the $k$ shortest paths, $k$ smallest spanning trees, and $k$ best matchings in weighted graphs.
Given a tree of weighted vertices, it is sometimes possible to break the tree into two equally-weighted subtrees within an allowable error. We give a fast algorithm that finds an edge which breaks the tree into equal-weight components or…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…
The minimum stretch spaning tree problem for a grah G is to find a spaning tree T of G such as that the maximum distance in T between two adjacent vertices is minimized. The minimum value of this optimization problem gives rise to a grpah…
In computer vision, we have the problem of creating graphs out of unstructured point-sets, i.e. the data graph. A common approach for this problem consists of building a triangulation which might not always lead to the best solution. Small…
We consider combinatorial problems that can be solved in polynomial time for graphs of bounded treewidth but where the order of the polynomial that bounds the running time is expected to depend on the treewidth bound. First we review some…
Standard algorithms for finding the shortest path in a graph require that the cost of a path be additive in edge costs, and typically assume that costs are deterministic. We consider the problem of uncertain edge costs, with potential…
The Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity in a given undirected graph. The problem is known to be NP-complete and W[2]-hard with respect to the desired eccentricity. We…
We study budget constrained network upgradeable problems. We are given an undirected edge weighted graph $G=(V,E)$ where the weight an edge $e \in E$ can be upgraded for a cost $c(e)$. Given a budget $B$ for improvement, the goal is to find…
The Minimum Spanning Tree problem (abbr. MSTP) is a well-known combinatorial optimization problem that has been extensively studied by the researchers in the field of evolutionary computing to theoretically analyze the optimization…
Spanning trees are an important primitive in many data analysis tasks, when a data set needs to be summarized in terms of its "skeleton", or when a tree-shaped graph over all observations is required for downstream processing. Popular…
In the area of evolutionary computation the calculation of diverse sets of high-quality solutions to a given optimization problem has gained momentum in recent years under the term evolutionary diversity optimization. Theoretical insights…
We investigate special cases of the quadratic minimum spanning tree problem (QMSTP) on a graph $G=(V,E)$ that can be solved as a linear minimum spanning tree problem. Characterization of such problems on graphs with special properties are…
We study minimum entropy submodular optimization, a common generalization of the minimum entropy set cover problem, studied earlier by Cardinal et al., and the submodular set cover problem. We give a general bound of the approximation…
In this paper we describe a randomized algorithm which returns a maximal spanning forest of an unknown {\em weighted} undirected graph making $O(n)$ $\mathsf{CUT}$ queries in expectation. For weighted graphs, this is optimal due to a result…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a spanning tree in which any two adjacent edges have distinct colors. Since finding such a tree is NP-hard in general,…