Related papers: The Global Packing Number for an Optical Network

In the Directed Disjoint Paths problem, we are given a digraph $D$ and a set of requests $\{(s_1, t_1), \ldots, (s_k, t_k)\}$, and the task is to find a collection of pairwise vertex-disjoint paths $\{P_1, \ldots, P_k\}$ such that each…

A covering path for a finite set $P$ of points in the plane is a polygonal path such that every point of $P$ lies on a segment of the path. The vertices of the path need not be at points of $P$. A covering path is plane if its segments do…

Let $G=(V,E)$ be a simple graph. A function $f:V\rightarrow \mathbb{N}\cup \{0\}$ is called a configuration of pebbles on the vertices of $G$ and the quantity $\vert f\vert=\sum_{u\in V}f(u)$ is called the weight of $f$ which is just the…

In this paper, we introduce a new concept in graph coloring, namely the \textit{packing total coloring}, which extends the idea of packing coloring to both the vertices and the edges of a given graph. More precisely, for a graph $G$, a…

We introduce a communication model for hybrid networks, where nodes have access to two different communication modes: a local mode where communication is only possible between specific pairs of nodes, and a global mode where communication…

Let $G=(V,E)$ be a graph. A subset $S \subseteq V$ is called a global dominating set of $G$, if it serves as a dominating set in both $G$ and its complement $\overline{G}$. We define two disjoint subsets $V_1,V_2 \subseteq V$ to form a…

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…

Let $S=(s_1,s_2,\ldots)$ be a non-decreasing sequence of positive integers. For a graph $G$ with vertex set $V(G)$, a labeling $\phi \colon V(G)\to \{1,\ldots,k\}$ is an $S$-packing $k$-coloring if, whenever two distinct vertices $u,v\in…

Given an undirected graph $G = (V, E)$, and a vertex $r\in V$, an $r$-acyclic orientation of $G$ is an orientation $OE$ of the edges of $G$ such that the digraph $OG = (V, OE)$ is acyclic and $r$ is the unique vertex with indegree equal to…

We present a new algorithm, which solves the problem of distributively finding a minimum diameter spanning tree of any (non-negatively) real-weighted graph $G = (V,E,\omega)$. As an intermediate step, we use a new, fast, linear-time…

Given an integer weighted bipartite graph $\{G=(U\sqcup V, E), w:E\rightarrow \mathbb{Z}\}$ we consider the problems of finding all the edges that occur in some minimum weight matching of maximum cardinality and enumerating all the minimum…

Given two $k$-graphs $H$ and $F$, a perfect $F$-packing in $H$ is a collection of vertex-disjoint copies of $F$ in $H$ which together cover all the vertices in $H$. In the case when $F$ is a single edge, a perfect $F$-packing is simply a…

We consider strongly-connected directed networks of identical synchronous, finite-state processors with in- and out-degree uniformly bounded by a network constant. Via a straightforward extension of Ostrovsky and Wilkerson's Backwards…

Global pooling is one of the most significant operations in many machine learning models and tasks, whose implementation, however, is often empirical in practice. In this study, we develop a novel and solid global pooling framework through…

We present a general technique, based on parametric search with some twist, for solving a variety of optimization problems on a set of semi-algebraic geometric objects of constant complexity. The common feature of these problems is that…

The paper is divided in to two parts. In the first part we present some new results for the \textit{routing via matching} model introduced by Alon et al\cite{5}. This model can be viewed as a communication scheme on a distributed network.…

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 fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing…

Given a simple graph $G$, a weight function $w:E(G)\rightarrow \mathbb{N} \setminus \{0\}$, and an orientation $D$ of $G$, we define $\mu^-(D) = \max_{v \in V(G)} w_D^-(v)$, where $w^-_D(v) = \sum_{u\in N_D^{-}(v)}w(uv)$. We say that $D$ is…

The paper presents a versatile library of analytic and quasi-analytic complex-valued wavelet packets (WPs) which originate from discrete splines of arbitrary orders. The real parts of the quasi-analytic WPs are the regular spline-based…