Related papers: Partition Expanders
Graph transformers have emerged as a promising architecture for a variety of graph learning and representation tasks. Despite their successes, though, it remains challenging to scale graph transformers to large graphs while maintaining…
The graph partitioning problem is widely used and studied in many practical and theoretical applications. The multilevel strategies represent today one of the most effective and efficient generic frameworks for solving this problem on…
The separation dimension of a graph $G$, written $\pi(G)$, is the minimum number of linear orderings of $V(G)$ such that every two nonincident edges are "separated" in some ordering, meaning that both endpoints of one edge appear before…
Simultaneous broadcasting of multiple messages from the same source vertex in synchronous networks is considered under restrictions that each vertex receives at most one message in a unit time step, every received message can be sent out…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
In this article, we show that the algorithm of maintaining expander decompositions in graphs undergoing edge deletions directly by removing sparse cuts repeatedly can be made efficient. Formally, for an $m$-edge undirected graph $G$, we say…
Graph separators are a ubiquitous tool in graph theory and computer science. However, in some applications, their usefulness is limited by the fact that the separator can be as large as $\Omega(\sqrt{n})$ in graphs with $n$ vertices. This…
A strongly separating path system in a graph $G$ is a collection $\mathcal{P}$ of paths in $G$ such that, for every two edges $e$ and $f$ of $G$, there is a paths in $\mathcal{P}$ with $e$ and not $f$, and vice-versa. The minimum number of…
We solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with <k^1/2>. In contrast, earlier results studying the problem in graphs with…
The work in this article is concerned with two different types of families of finite sets: separating families and splitting families (they are also called "systems"). These families have applications in combinatorial search, coding theory,…
Entity Set Expansion is an important NLP task that aims at expanding a small set of entities into a larger one with items from a large pool of candidates. In this paper, we propose GausSetExpander, an unsupervised approach based on optimal…
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star…
Partitioning a graph using graph separators, and particularly clique separators, are well-known techniques to decompose a graph into smaller units which can be treated independently. It was previously known that the treewidth was bounded…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the…
The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…
Hopsets and spanners are fundamental graph structures, playing a key role in shortest path computation, distributed communication, and more. A (near-exact) hopset for a given graph $G$ is a (small) subset of weighted edges $H$ that when…
We study separating systems of the edges of a graph where each member of the separating system is a path. We conjecture that every $n$-vertex graph admits a separating path system of size $O(n)$ and prove this in certain interesting special…
The number partition problem is a well-known problem, which is one of 21 Karp's NP-complete problems \cite{karp}. The partition function is a boolean function that is equivalent to the number partition problem with number range restricted.…
We present a different way to obtain generators of metric spaces having the property that the ``position'' of every element of the space is uniquely determined by the distances from the elements of the generators. Specifically we introduce…