Related papers: Complexity Analysis of 2-Heterogeneous Minimum Spa…
This work considers the problem of user association to small-cell base stations (SBSs) in a heterogeneous and small-cell network (HetSNet). Two optimization problems are investigated, which are maximizing the set of associated users to the…
In real life, it is always an urge to reach our goal in minimum effort i.e., it should have a minimum constrained path. The path may be shortest route in practical life, either physical or electronic medium. The scenario is to represents…
We investigate the complexity of the reachability problem for (deep) neural networks: does it compute valid output given some valid input? It was recently claimed that the problem is NP-complete for general neural networks and…
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…
In this paper, we consider the minimum spanning tree problem (for short, MSTP) on an arbitrary set of $n$ points of $d$-dimensional space in $l_1$-norm. For this problem, for each fixed $d\geq 2$, there is a known algorithm of the…
This article studies the Minimum Spanning Tree Problem under Explorable Uncertainty as well as a related vertex uncertainty version of the problem. We particularly consider special instance types, including cactus graphs, for which we…
Bounded-angle (minimum) spanning trees were first introduced in the context of wireless networks with directional antennas. They are reminiscent of bounded-degree spanning trees, which have received significant attention. Let $P =…
This paper give a simple linear-time algorithm that, given a weighted digraph, finds a spanning tree that simultaneously approximates a shortest-path tree and a minimum spanning tree. The algorithm provides a continuous trade-off: given the…
This paper studies Minimum Spanning Trees under incomplete information for its vertices. We assume that no information is available on the precise placement of vertices so that it is only known that vertices belong to some neighborhoods…
The complexity of the maximum common connected subgraph problem in partial $k$-trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial $2$-trees. On the other…
Given a satisfiable instance of 1-in-3 SAT, it is NP-hard to find a satisfying assignment for it, but it may be possible to efficiently find a solution subject to a weaker (not necessarily Boolean) predicate than `1-in-3'. There is a…
We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in…
The vertex cover problem is one of the most important and intensively studied combinatorial optimization problems. Khot and Regev (2003) proved that the problem is NP-hard to approximate within a factor $2 - \epsilon$, assuming the Unique…
A set $G$ of points on a 1.5-dimensional terrain, also known as an $x$-monotone polygonal chain, is said to guard the terrain if any point on the terrain is 'seen' by a point in $G$. Two points on the terrain see each other if and only if…
We show that the spanning tree congestion problem is NP-complete even for proper interval graphs of linear clique-width at most 4.
The problem of approximating a dense matrix by a product of sparse factors is a fundamental problem for many signal processing and machine learning tasks. It can be decomposed into two subproblems: finding the position of the non-zero…
We propose a simple and natural approximation algorithm for the problem of finding a 2-edge-connected spanning subgraph of minimum total edge cost in a graph. The algorithm maintains a spanning forest starting with an empty edge set. In…
The Surjective Homomorphism problem is to test whether a given graph G called the guest graph allows a vertex-surjective homomorphism to some other given graph H called the host graph. The bijective and injective homomorphism problems can…
The Optimal Morse Matching (OMM) problem asks for a discrete gradient vector field on a simplicial complex that minimizes the number of critical simplices. It is NP-hard and has been studied extensively in heuristic, approximation, and…