The Power of Two Matrices in Spectral Algorithms for Community Recovery
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A hallmark of graph neural networks is their ability to distinguish the isomorphism class of their inputs. This study derives hardness results for the classification variant of graph isomorphism in the message-passing model (MPNN). MPNN encompasses the maj ...
Queries to detect isomorphic subgraphs are important in graph-based data management. While the problem of subgraph isomorphism search has received considerable attention for the static setting of a single query, or a batch thereof, existing approaches do n ...
Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating distinct subsets of row ...
Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study th ...
Graph processing systems are used in a wide variety of fields, ranging from biology to social networks.
Algorithms to mine graphs incur many random accesses, and the sparse nature of the graphs of interest, exacerbates this. As DRAM sustains high bandwidt ...
This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e. with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so far has focused on ...
Given a graph H and a set of graphs F, let ex(n, H, F) denote the maximum possible number of copies of H in an T-free graph on n vertices. We investigate the function ex(n, H, F), when H and members of F are cycles. Let C-k denote the cycle of length k and ...
A sparsifier of a graph G (Bencztir and Karger; Spielman and Teng) is a sparse weighted subgraph (G) over tilde that approximately retains the same cut structure of G. For general graphs, non-trivial sparsification is possible only by using weighted graphs ...
A clique covering of a graph G is a set of cliques of G such that any edge of G is contained in one of these cliques, and the weight of a clique covering is the sum of the sizes of the cliques in it. The sigma clique cover number scc(G) of a graph G, is de ...
The problem of generating a minimal implementation of a given Boolean function is called exact synthesis. The parameter to be minimized is often the total number of gates used for the implementation. The exact synthesis engine is considered an essential to ...
