Related papers: Partitioning Hypergraphs is Hard: Models, Inapprox…
This work addresses the NP-Hard problem of acyclic directed acyclic graph (DAG) partitioning problem. The acyclic partitioning problem is defined as partitioning the vertex set of a given directed acyclic graph into disjoint and…
Partitioning large matrices is an important problem in distributed linear algebra computing (used in ML among others). Briefly, our goal is to perform a sequence of matrix algebra operations in a distributed manner (whenever possible) on…
An assumption that researchers have often used to model interference in a wireless network is the unit disk graph model. While many theoretical results and performance guarantees have been obtained under this model, an open research…
This paper initiates the study of the classic balanced graph partitioning problem from an online perspective: Given an arbitrary sequence of pairwise communication requests between $n$ nodes, with patterns that may change over time, the…
The problem of multiway partitioning of an undirected graph is considered. A spectral method is used, where the k > 2 largest eigenvalues of the normalized adjacency matrix (equivalently, the k smallest eigenvalues of the normalized graph…
The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…
Many load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary…
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…
Hypergraphs allow modeling problems with multi-way high-order relationships. However, the computational cost of most existing hypergraph-based algorithms can be heavily dependent upon the input hypergraph sizes. To address the…
We consider the problem of partitioning the node set of a graph into $k$ sets of given sizes in order to \emph{minimize the cut} obtained using (removing) the $k$-th set. If the resulting cut has value $0$, then we have obtained a vertex…
In order to improve system performance efficiently, a number of systems choose to equip multi-core and many-core processors (such as GPUs). Due to their discrete memory these heterogeneous architectures comprise a distributed system within…
Hypergraph partitioning is used in many problem domains including VLSI design, linear algebra, Boolean satisfiability, and data mining. Most versions of this problem are NP-complete or NP-hard, so practical hypergraph partitioners generate…
We consider the following "multiway cut packing" problem in undirected graphs: we are given a graph G=(V,E) and k commodities, each corresponding to a set of terminals located at different vertices in the graph; our goal is to produce a…
Influence maximization in complex networks, i.e., maximizing the size of influenced nodes via selecting K seed nodes for a given spreading process, has attracted great attention in recent years. However, the influence maximization problem…
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…
Balanced hypergraph partitioning is a classical NP-hard optimization problem with applications in various domains such as VLSI design, simulating quantum circuits, optimizing data placement in distributed databases or minimizing…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
We present semi-streaming algorithms for basic graph problems that have optimal per-edge processing times and therefore surpass all previous semi-streaming algorithms for these tasks. The semi-streaming model, which is appropriate when…
Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance…
The NP-hard maximum value preordering problem is both a joint relaxation and a hybrid of the clique partition problem (a clustering problem) and the partial ordering problem. Toward approximate solutions and lower bounds, we introduce a…