Related papers: Bidirected minimum Manhattan network problem
The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…
Given two points s and t in the plane and a set of obstacles defined by closed curves, what is the minimum number of obstacles touched by a path connecting s and t? This is a fundamental and well-studied problem arising naturally in…
We present the first exact polynomial time algorithm for constructing optimal geometric bottleneck 2-connected Steiner networks containing at most $k$ Steiner points, where $k>2$ is a constant. Given a set of $n$ vertices embedded in an…
We show that the Minimal Length-Bounded L-But problem can be computed in linear time with respect to L and the tree-width of the input graph as parameters. In this problem the task is to find a set of edges of a graph such that after…
We consider minimization of a sum of convex objective functions where the components of the objective are available at different nodes of a network and nodes are allowed to only communicate with their neighbors. The use of distributed…
Consider a setting where possibly sensitive information sent over a path in a network is visible to every {neighbor} of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a…
In this paper we study the problem of model reduction of linear network systems. We aim at computing a reduced order stable approximation of the network with the same topology and optimal w.r.t. H2 norm error approximation. Our approach is…
We introduce a new bilevel version of the classic shortest path problem and completely characterize its computational complexity with respect to several problem variants. In our problem, the leader and the follower each control a subset of…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
We study the 2-Disjoint Shortest Paths (2-DSP) problem: given a directed weighted graph and two terminal pairs $(s_1,t_1)$ and $(s_2,t_2)$, decide whether there exist vertex-disjoint shortest paths between each pair. Building on recent…
For the Weber problem of construction of the minimal cost planar weighted network connecting four terminals with two extra facilities, the solution by radicals is proposed. The conditions for the existence of the network in the assumed…
We consider two orientation problems in a graph, namely the minimization of the sum of all the shortest path lengths and the minimization of the diameter. We show that it is NP-complete to decide whether a graph has an orientation such that…
On an assigned graph, the problem of Multi-Agent Pathfinding (MAPF) consists in finding paths for multiple agents, avoiding collisions. Finding the minimum-length solution is known to be NP-hard, and computation times grows exponentially…
In the Connected Dominating Set problem we are given a graph $G=(V,E)$ and seek a minimum size dominating set $S \subseteq V$ such that the subgraph $G[S]$ of $G$ induced by $S$ is connected. In the $2$-Edge-Connected Dominating Set problem…
A multimodal network encodes relationships between the same set of nodes in multiple settings, and network alignment is a powerful tool for transferring information and insight between a pair of networks. We propose a method for multimodal…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Given a set $P$ of $n$ points in the plane, we solve the problems of constructing a geometric planar graph spanning $P$ 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2…
In most of the shortest path problems like vehicle routing problems and network routing problems, we only need an efficient path between two points source and destination, and it is not necessary to calculate the shortest path from source…
We consider a bilevel program involving a linear lower level problem with left-hand-side perturbation. We then consider the Karush-Kuhn-Tucker reformulation of the problem and subsequently build a tractable optimization problem with linear…
In this paper, we propose a distributed algorithm for the minimum dominating set problem. For some especial networks, we prove theoretically that the achieved answer by our proposed algorithm is a constant approximation factor of the exact…