Related papers: Restorable Shortest Path Tiebreaking for Edge-Faul…
Let $G$ be an $n$-node and $m$-edge positively real-weighted undirected graph. For any given integer $f \ge 1$, we study the problem of designing a sparse \emph{f-edge-fault-tolerant} ($f$-EFT) $\sigma${\em -approximate single-source…
In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest s-t path P such that no path in X is a subpath of P. Path P…
The labeled stochastic block model is a random graph model representing networks with community structure and interactions of multiple types. In its simplest form, it consists of two communities of approximately equal size, and the edges…
We initiate the study of the shortest reconfiguration problem for independent sets under the adjacency relation derived from the independent set polytope. Given a graph and two independent sets, the problem asks for a shortest sequence…
Imagine that unlabelled tokens are placed on the edges of a graph, such that no two tokens are placed on incident edges. A token can jump to another edge if the edges having tokens remain independent. We study the problem of determining the…
The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…
Consider the following problem: given a graph with edge costs and a subset Q of vertices, find a minimum-cost subgraph in which there are two edge-disjoint paths connecting every pair of vertices in Q. The problem is a failure-resilient…
Given an undirected graph $G=(V,E)$ with positive edge lengths and two vertices $s$ and $t$, the next-to-shortest path problem is to find an $st$-path which length is minimum amongst all $st$-paths strictly longer than the shortest path…
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…
Graph theory is increasingly commonly utilised in genetics, proteomics and neuroimaging. In such fields, the data of interest generally constitute weighted graphs. Analysis of such weighted graphs often require the integration of…
We formulate and study the thinnest path problem in wireless ad hoc networks. The objective is to find a path from a source to its destination that results in the minimum number of nodes overhearing the message by a judicious choice of…
Provenance embedding algorithms are well known for tracking the footprints of information flow in wireless networks. Recently, low-latency provenance embedding algorithms have received traction in vehicular networks owing to strict…
We study a natural online variant of the replacement path problem. The \textit{replacement path problem} asks to find for a given graph $G = (V,E)$, two designated vertices $s,t\in V$ and a shortest $s$-$t$ path $P$ in $G$, a…
We present a message-passing algorithm to solve the edge disjoint path problem (EDP) on graphs incorporating under a unique framework both traffic optimization and path length minimization. The min-sum equations for this problem present an…
We study a large family of graph covering problems, whose definitions rely on distances, for graphs of bounded cyclomatic number (that is, the minimum number of edges that need to be removed from the graph to destroy all cycles). These…
We study the problem of sampling and reconstruction of bandlimited graph signals where the objective is to select a node subset of prescribed cardinality that ensures interpolation of the original signal with the lowest reconstruction…
The basic goal of survivable network design is to construct low-cost networks which preserve a sufficient level of connectivity despite the failure or removal of a few nodes or edges. One of the most basic problems in this area is the…
Resilient computation in all-to-all-communication models has attracted tremendous attention over the years. Most of these works assume the classical faulty model which restricts the total number of corrupted edges (or vertices) by some…
As large graph datasets become increasingly common across many fields, sampling is often needed to reduce the graphs into manageable sizes. This procedure raises critical questions about representativeness as no sample can capture the…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…