相关论文: On fractionality of the path packing problem

We examine the dynamic network flow problem under the assumption that the flow consists of discrete units. The dynamic network flow problem is commonly addressed in the context of developing evacuation plans, where the flow is typically…

We study network design with a cost structure motivated by redundancy in data traffic. We are given a graph, g groups of terminals, and a universe of data packets. Each group of terminals desires a subset of the packets from its respective…

Real networks are vulnerable to random failures and malicious attacks. However, when a node is harmed or damaged, it may remain partially functional, which helps to maintain the overall network structure and functionality. In this paper, we…

In this paper we study path integral for a single spinless particle on a star graph with N edges, whose vertex is known to be described by U(N) family of boundary conditions. After carefully studying the free particle case, both at the…

The dicycle transversal number t(D) of a digraph D is the minimum size of a dicycle transversal of D, i. e. a set T of vertices of D such that D-T is acyclic. We study the following problem: Given a digraph D, decide if there is a dicycle B…

The boxicity of a graph $G$ is the minimum non-negative integer $k$ such that $G$ can be isomorphic to the intersection graph of a family of boxes in Euclidean $k$-space, where a box in Euclidean $k$-space is the Cartesian product of $k$…

Network flow problems, which involve distributing traffic such that the underlying infrastructure is used effectively, are ubiquitous in transportation and logistics. Among them, the general Multi-Commodity Network Flow (MCNF) problem…

We introduce a variant of the multiway cut that we call the min-max connected multiway cut. Given a graph $G=(V,E)$ and a set $\Gamma\subseteq V$ of $t$ terminals, partition $V$ into $t$ parts such that each part is connected and contains…

We propose in the paper a novel framework for using a common control input to simultaneously steer an infinite ensemble of networked control systems. We address the problem of co-designing information flow topology and network dynamics of…

A path partition (also referred to as a linear forest) of a graph $G$ is a set of vertex-disjoint paths which together contain all the vertices of $G$. An isolated vertex is considered to be a path in this case. The path partition…

This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…

We consider a network (that is capable of network coding) with a set of sources and terminals, where each terminal is interested in recovering the sum of the sources. Considering directed acyclic graphs with unit capacity edges and…

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…

Given a complete graph with positive weights on its edges, we define the weight of a subset of edges as the product of weights of the edges in the subset and consider sums (partition functions) of weights over subsets of various kinds:…

The Flow Decomposition problem, which asks for the smallest set of weighted paths that "covers" a flow on a DAG, has recently been used as an important computational step in transcript assembly. We prove the problem is in FPT when…

We apply percolation theory to a recently proposed measure of fragmentation $F$ for social networks. The measure $F$ is defined as the ratio between the number of pairs of nodes that are not connected in the fragmented network after…

Wasserstein gradient flows on probability measures have found a host of applications in various optimization problems. They typically arise as the continuum limit of exchangeable particle systems evolving by some mean-field interaction…

The directions of an infinite graph $G$ are a tangle-like description of its ends: they are choice functions that choose compatibly for all finite vertex sets $X\subseteq V(G)$ a component of $G-X$. Although every direction is induced by a…

Let $F$ be a strictly $1$-balanced $k$-graph on $s$ vertices with $t$ edges and $\delta_{F,d}^T$ be the infimum of $\delta>0$ such that for every $\alpha>0$ and sufficiently large $n\in \mathbb{N}$, every $k$-graph system $\mathbf…

A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$…