Related papers: Graph partitioning using matrix differential equat…
We study the minimum cut problem in weighted undirected graphs using variational quantum algorithms in which only feasible cut configurations are explored. Although minimum cut admits efficient classical solutions, it is a fundamental…
We investigate connections between the symmetries (automorphisms) of a graph and its spectral properties. Whenever a graph has a symmetry, i.e. a nontrivial automorphism $\phi$, it is possible to use $\phi$ to decompose any matrix…
In this paper, we develop semi-external and external memory algorithms for graph partitioning and clustering problems. Graph partitioning and clustering are key tools for processing and analyzing large complex networks. We address both…
We study the parameterized complexity of a broad class of problems called "local graph partitioning problems" that includes the classical fixed cardinality problems as max k-vertex cover, k-densest subgraph, etc. By developing a technique…
We study a general class of problems called F-deletion problems. In an F-deletion problem, we are asked whether a subset of at most $k$ vertices can be deleted from a graph $G$ such that the resulting graph does not contain as a minor any…
We study the balanced $k$-way hypergraph partitioning problem, with a special focus on its practical applications to manycore scheduling. Given a hypergraph on $n$ nodes, our goal is to partition the node set into $k$ parts of size at most…
Let $\Pi$ be a hereditary graph class. The problem of deletion to $\Pi$, takes as input a graph $G$ and asks for a minimum number (or a fixed integer $k$) of vertices to be deleted from $G$ so that the resulting graph belongs to $\Pi$. This…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
In this paper, we investigate the approximability of two node deletion problems. Given a vertex weighted graph $G=(V,E)$ and a specified, or "distinguished" vertex $p \in V$, MDD(min) is the problem of finding a minimum weight vertex set $S…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning…
Graph embedding learns low-dimensional representations for nodes in a graph and effectively preserves the graph structure. Recently, a significant amount of progress has been made toward this emerging research area. However, there are…
We study the problem of deleting a minimum cost set of vertices from a given vertex-weighted graph in such a way that the resulting graph has no induced path on three vertices. This problem is often called cluster vertex deletion in the…
Graphs are naturally sparse objects that are used to study many problems involving networks, for example, distributed learning and graph signal processing. In some cases, the graph is not given, but must be learned from the problem and…
Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…
We tackle three optimization problems in which a colored graph, where each node is assigned a color, must be partitioned into colorful connected components. A component is defined as colorful if each color appears at most once. The problems…
Partitioning a graph into blocks of roughly equal weight while cutting only few edges is a fundamental problem in computer science with numerous practical applications. While shared-memory parallel partitioners have recently matured to…
Graph Partitioning is a critical problem in numerous scientific and engineering domains including social network analysis, VLSI design, and many more. Spectral methods are known to produce quality partitions while minimizing edge cuts for a…