Related papers: Computational Approaches for Zero Forcing and Rela…
In this paper, we propose an inertial forward backward splitting algorithm to compute a zero of the sum of two monotone operators, with one of the two operators being co-coercive. The algorithm is inspired by the accelerated gradient method…
Motivated by a conjecture from the automated conjecturing program TxGraffiti, in this paper the relationship between the zero forcing number, $Z(G)$, and the vertex independence number, $\alpha(G)$, of cubic and subcubic graphs is explored.…
Although research on the control of networked systems has grown considerably, graph-theoretic and algorithmic studies on matrix-weighted graphs remain limited. To bridge this gap in the literature, this work introduces two algorithms-the…
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 paper proves a conjecture generated by the artificial intelligence conjecturing program called \emph{TxGraffiti}. More specifically, we show that if $G$ is a connected, cubic, and claw-free graph, then $Z(G) \le \gamma(G) + 2$, where…
Graph embedding has become an increasingly important technique for analyzing graph-structured data. By representing nodes in a graph as vectors in a low-dimensional space, graph embedding enables efficient graph processing and analysis…
Deduction is a recently introduced graph searching process in which searchers clear the vertex set of a graph with one move each, with each searcher's movement determined by which of its neighbors are protected by other searchers. In this…
In this paper, we study minimal (with respect to inclusion) zero forcing sets. We first investigate when a graph can have polynomially or exponentially many distinct minimal zero forcing sets. We also study the maximum size of a minimal…
Zero forcing is a process on graphs in which a color change rule is used to force vertices to become blue. The amount of time taken for all vertices in the graph to become blue is the propagation time. Throttling minimizes the sum of the…
I will present a way to implement graph algorithms which is different from traditional methods. This work was motivated by the belief that some ideas from software engineering should be applied to graph algorithms. Re-usability of software…
This paper describes a unified method solving for inverse, forward, and hybrid dynamics problems for robotic manipulators with either open kinematic chains or closed kinematic loops based on factor graphs. Manipulator dynamics is considered…
There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is defined as the largest $i$ such that the $i$-th critical…
Probabilistic zero forcing is a graph coloring process in which blue vertices "infect" (color blue) white vertices with a probability proportional to the number of neighboring blue vertices. We introduce reversion probabilistic zero forcing…
We introduce randomized zero forcing (RZF), a stochastic color-change process on directed graphs in which a white vertex turns blue with probability equal to the fraction of its incoming neighbors that are blue. Unlike probabilistic zero…
While graphs and abstract data structures can be large and complex, practical instances are often regular or highly structured. If the instance has sufficient structure, we might hope to compress the object into a more succinct…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…
A zero forcing set is a set $S$ of vertices of a graph $G$, called forced vertices of $G$, which are able to force the entire graph by applying the following process iteratively: At any particular instance of time, if any forced vertex has…
Let $G$ be a graph that admits a perfect matching. A {\sf forcing set} for a perfect matching $M$ of $G$ is a subset $S$ of $M$, such that $S$ is contained in no other perfect matching of $G$. This notion originally arose in chemistry in…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…