Related papers: Trapping problem on star-type graphs with applicat…
Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…
This work presents a study of star covers on graphs. Unlike traditional formulations that minimize the number of stars, our aim is to optimize the number of bipartite components used in the cover. This problem, motivated by a symmetric…
In the Asymmetric Traveling Salesperson Problem (ATSP) the goal is to find a closed walk of minimum cost in a directed graph visiting every vertex. We consider the approximability of ATSP on topologically restricted graphs. It has been…
Attention mechanisms have made significant strides in graph learning, yet they still exhibit notable limitations: local attention faces challenges in capturing long-range information due to the inherent problems of the message-passing…
Data aggregation is a fundamental primitive in distributed computing wherein a network computes a function of every nodes' input. However, while compute time is non-negligible in modern systems, standard models of distributed computing do…
Graph rigidity theory studies the capability of a graph embedded in the Euclidean space to constrain its global geometric shape via local constraints among nodes and edges, and has been widely exploited in network localization and formation…
The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the location of the robber. We present a novel graph parameter called…
One of the most fundamental problems in Computer Science is the Knapsack problem. Given a set of n items with different weights and values, it asks to pick the most valuable subset whose total weight is below a capacity threshold T. Despite…
A target set selection model is a graph $G$ with a threshold function $\tau:V\to \mathbb{N}$ upper-bounded by the vertex degree. For a given model, a set $S_0\subseteq V(G)$ is a target set if $V(G)$ can be partitioned into non-empty…
Level-sensitive latches are widely used in high- performance designs. For such circuits efficient statistical timing analysis algorithms are needed to take increasing process vari- ations into account. But existing methods solving this…
A graph $G$ is contractible to a graph $H$ if there is a set $X \subseteq E(G)$, such that $G/X$ is isomorphic to $H$. Here, $G/X$ is the graph obtained from $G$ by contracting all the edges in $X$. For a family of graphs $\cal F$, the…
Several modern applications involve huge graphs and require fast answers to reachability queries. In more than two decades since first proposals, several approaches have been presented adopting on-line searches, hop labelling or transitive…
The bondage number of a graph is the smallest number of its edges whose removal results in a graph having a larger domination number. We provide constant upper bounds for the bondage number of graphs on topological surfaces, improve upper…
Computing paths in graph structures is a fundamental operation in a wide range of applications, from transportation networks to data analysis. The beer path problem, which captures the option of visiting points of interest, such as gas…
The All-Pairs Shortest Paths (APSP) problem is one of the fundamental problems in theoretical computer science. It asks to compute the distance matrix of a given $n$-vertex graph. We revisit the classical problem of maintaining the distance…
In a Subgraph Problem we are given some graph and want to find a feasible subgraph that optimizes some measure. We consider Multistage Subgraph Problems (MSPs), where we are given a sequence of graph instances (stages) and are asked to find…
We consider the fundamental problems of determining the rooted and global edge and vertex connectivities (and computing the corresponding cuts) in directed graphs. For rooted (and hence also global) edge connectivity with small integer…
Graph-theoretic tools and techniques have seen wide use in the multi-agent systems literature, and the unpredictable nature of some multi-agent communications has been successfully modeled using random communication graphs. Across both…
We study two "above guarantee" versions of the classical Longest Path problem on undirected and directed graphs and obtain the following results. In the first variant of Longest Path that we study, called Longest Detour, the task is to…
In modern applications of graphs algorithms, where the graphs of interest are large and dynamic, it is unrealistic to assume that an input representation contains the full information of a graph being studied. Hence, it is desirable to use…