相关论文: Fast and Compact Graph Cuts for the Boykov-Kolmogo…
We study graph partitioning problems from a min-max perspective, in which an input graph on n vertices should be partitioned into k parts, and the objective is to minimize the maximum number of edges leaving a single part. The two main…
We present a new approach called GR (Graph Reduction) algorithm for searching loop-less k-shortest paths (1st to k-th shortest paths) in a graph based on graph reduction. Let a source vertex and a target vertex of k-shortest paths be v_s…
We present a practically efficient algorithm for maintaining a global minimum cut in large dynamic graphs under both edge insertions and deletions. While there has been theoretical work on this problem, our algorithm is the first…
This paper presents an $O^{*}(1.42^{n})$ time algorithm for the Maximum Cut problem on split graphs, along with a subexponential time algorithm for its decision variant.
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
The most commonly used method to tackle the graph partitioning problem in practice is the multilevel approach. During a coarsening phase, a multilevel graph partitioning algorithm reduces the graph size by iteratively contracting nodes and…
We introduce and study Weighted Min $(s,t)$-Cut Prevention, where we are given a graph $G=(V,E)$ with vertices $s$ and $t$ and an edge cost function and the aim is to choose an edge set $D$ of total cost at most $d$ such that $G$ has no…
We consider the classical Minimum Balanced Cut problem: given a graph $G$, compute a partition of its vertices into two subsets of roughly equal volume, while minimizing the number of edges connecting the subsets. We present the first {\em…
We present a general method of designing fast approximation algorithms for cut-based minimization problems in undirected graphs. In particular, we develop a technique that given any such problem that can be approximated quickly on trees,…
We consider the Minimum Steiner Cut problem on undirected planar graphs with non-negative edge weights. This problem involves finding the minimum cut of the graph that separates a specified subset $X$ of vertices (terminals) into two parts.…
We present a \emph{deterministic exact algorithm} for the \emph{minimum $k$-cut problem} on simple graphs. Our approach combines the \emph{principal sequence of partitions (PSP)}, derived canonically from ideal loads, with a single level of…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…
In the classic Minimum Bisection problem we are given as input a graph $G$ and an integer $k$. The task is to determine whether there is a partition of $V(G)$ into two parts $A$ and $B$ such that $||A|-|B|| \leq 1$ and there are at most $k$…
In the simultaneous Max-Cut problem, we are given $k$ weighted graphs on the same set of $n$ vertices, and the goal is to find a cut of the vertex set so that the minimum, over the $k$ graphs, of the cut value is as large as possible.…
We design two incremental algorithms for computing an inclusion-minimal completion of an arbitrary graph into a cograph. The first one is able to do so while providing an additional property which is crucial in practice to obtain…
We consider the Hypergraph-$k$-cut problem. The input consists of a hypergraph $G=(V,E)$ with non-negative hyperedge-costs $c: E\rightarrow R_+$ and a positive integer $k$. The objective is to find a least-cost subset $F\subseteq E$ such…
We study the \textsc{$\alpha$-Fixed Cardinality Graph Partitioning ($\alpha$-FCGP)} problem, the generic local graph partitioning problem introduced by Bonnet et al. [Algorithmica 2015]. In this problem, we are given a graph $G$, two…
Given an undirected, weighted graph, with $n$ vertices and $m$ edges, and two special vertices $s$ and $t$, the problem is to find the shortest path between them. We give two bounded-error quantum algorithms with improved runtime in the…
Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is $\gamma$-quasi-clique (QC), where each vertex connects at least a fraction $\gamma$ of the other vertices inside.…