Related papers: Lexico-minimum Replica Placement in Multitrees
In SDN stateful data planes, switches can execute algorithms to process traffic based on local states. This approach permits to offload decisions from the controller to the switches, thus to reduce the latency to react to network events. We…
Planning for multi-robot teams in complex environments is a challenging problem, especially when these teams must coordinate to accomplish a common objective. In general, optimal solutions to these planning problems are computationally…
Allocating physical layer resources to users based on channel quality, buffer size, requirements and constraints represents one of the central optimization problems in the management of radio resources. The solution space grows…
The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or…
We consider the indirect covering subtree problem (Kim et al., 1996). The input is an edge weighted tree graph along with customers located at the nodes. Each customer is associated with a radius and a penalty. The goal is to locate a…
This paper addresses the problem of coordination of a fleet of mobile robots - the problem of finding an optimal set of collision-free trajectories for individual robots in the fleet. Many approaches have been introduced during the last…
We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant…
In the first paper (part I) of this series of two, we introduce four novel definitions of the ODT problems: three for size-constrained trees and one for depth-constrained trees. These definitions are stated unambiguously through executable…
This paper is concerned with a constrained optimization problem over a directed graph (digraph) of nodes, in which the cost function is a sum of local objectives, and each node only knows its local objective and constraints. To…
We continue the study of $\delta$-dispersion, a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many…
In literature, Clustered Shortest-Path Tree Problem (CluSPT) is an NP-hard problem. Previous studies often search for an optimal solution in relatively large space. To enhance the performance of the search process, two approaches are…
We revisit the issue of low-distortion embedding of metric spaces into the line, and more generally, into the shortest path metric of trees, from the parameterized complexity perspective.Let $M=M(G)$ be the shortest path metric of an edge…
Treewidth is a useful tool in designing graph algorithms. Although many NP-hard graph problems can be solved in linear time when the input graphs have small treewidth, there are problems which remain hard on graphs of bounded treewidth. In…
We study the computational complexity of optimally solving multi-robot path planning problems on planar graphs. For four common time- and distance-based objectives, we show that the associated path optimization problems for multiple robots…
In the Weighted Treewidth-$\eta$ Deletion problem we are given a node-weighted graph $G$ and we look for a vertex subset $X$ of minimum weight such that the treewidth of $G-X$ is at most $\eta$. We show that Weighted Treewidth-$\eta$…
In distributed storage systems reliability is achieved through redundancy stored at different nodes in the network. Then a data collector can reconstruct source information even though some nodes fail. To maintain reliability, an autonomous…
Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…
Graph-modification problems, where we modify a graph by adding or deleting vertices or edges or contracting edges to obtain a graph in a {\it simpler} class, is a well-studied optimization problem in all algorithmic paradigms including…