Related papers: Approximating Cumulative Pebbling Cost is Unique G…
Sampling is a fundamental topic in graph signal processing, having found applications in estimation, clustering, and video compression. In contrast to traditional signal processing, the irregularity of the signal domain makes selecting a…
A total weighting of a graph $G$ is a mapping $f$ which assigns to each element $z \in V(G) \cup E(G)$ a real number $f(z)$ as its weight. The vertex sum of $v$ with respect to $f$ is $\phi_f(v)=\sum_{e \in E(v)}f(e)+f(v)$. A total…
For any configuration of pebbles on the nodes of a graph, a pebbling move replaces two pebbles on one node by one pebble on an adjacent node. A cover pebbling is a move sequence ending with no empty nodes. The number of pebbles needed for a…
Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…
The biclique partition number $(\text{bp})$ of a graph $G$ is referred to as the least number of complete bipartite (biclique) subgraphs that are required to cover the edges of the graph exactly once. In this paper, we show that the…
We study the complexity of the following related computational tasks concerning a fixed countable graph G: 1. Does a countable graph H provided as input have a(n induced) subgraph isomorphic to G? 2. Given a countable graph H that has a(n…
We investigate the complexity and approximability of the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value…
Conductance-based graph clustering has been recognized as a fundamental operator in numerous graph analysis applications. Despite the significant success of conductance-based graph clustering, existing algorithms are either hard to obtain…
The problems of determining the minimum-sized \emph{identifying}, \emph{locating-dominating} and \emph{open locating-dominating codes} of an input graph are special search problems that are challenging from both theoretical and…
Approximate random $k$-colouring of a graph $G$ is a well studied problem in computer science and statistical physics. It amounts to constructing a $k$-colouring of $G$ which is distributed close to {\em Gibbs distribution} in polynomial…
We investigate the Sobolev IPM problem for probability measures supported on a graph metric space. Sobolev IPM is an important instance of integral probability metrics (IPM), and is obtained by constraining a critic function within a unit…
In this paper we completely describe the unital compressed commuting graph of the ring $\mathcal{M}_3(\mathrm{GF}(p))$ of $3 \times 3$ matrices over the finite prime field $\mathrm{GF}(p)$. To achieve this we combine methods from linear…
We study fundamental graph problems such as graph connectivity, minimum spanning forest (MSF), and approximate maximum (weight) matching in a distributed setting. In particular, we focus on the Adaptive Massively Parallel Computation (AMPC)…
We aim to find orientations of mixed graphs optimizing the total reachability, a problem that has applications in causality and biology. For given a digraph $D$, we use $P(D)$ for the set of ordered pairs of distinct vertices in $V(D)$ and…
In the cops and robber games played on a simple graph $G$, Aigner and Fromme's lemma states that one cop can guard a shortest path in the sense that the robber cannot enter this path without getting caught after finitely many steps. In this…
Given a graph $G=(V, E)$ and and a proper labeling $f$ from $V$ to $\{1, ..., n\}$, we define $B(f)$ as the maximum absolute difference between $f(u)$ and $f(v)$ where $(u,v)\in E$. The bandwidth of $G$ is the minimum $B(f)$ for all $f$.…
Maximal clique enumeration is a fundamental graph mining task, but its utility is often limited by computational intractability and highly redundant output. To address these challenges, we introduce \emph{$\rho$-dense aggregators}, a novel…
Iterative Proportional Fitting (IPF), combined with EM, is commonly used as an algorithm for likelihood maximization in undirected graphical models. In this paper, we present two iterative algorithms that generalize upon IPF. The first one…
We prove that any finite abelian group $G$ contains a collection of not too many subsets with a special structure, so that for every subset $A$ of $G$ with a small doubling, there is a member $F$ of the collection that is fully contained in…
In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of…