相关论文: A faster algorithm for Cops and Robbers

Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…

We consider a connected undirected graph $G(n,m)$ with $n$ nodes and $m$ edges. A $k$-dominating set $D$ in $G$ is a set of nodes having the property that every node in $G$ is at most $k$ edges away from at least one node in $D$. Finding a…

We study a problem where k autonomous mobile agents are initially located on distinct nodes of a weighted graph (with n nodes and m edges). Each autonomous mobile agent has a predefined velocity and is only allowed to move along the edges…

We study the computational complexity of a perfect-information two-player game proposed by Aigner and Fromme. The game takes place on an undirected graph where n simultaneously moving cops attempt to capture a single robber, all moving at…

The cyclability of a graph is the maximum integer $k$ for which every $k$ vertices lie on a cycle. The algorithmic version of the problem, given a graph $G$ and a non-negative integer $k,$ decide whether the cyclability of $G$ is at least…

Connectivity related concepts are of fundamental interest in graph theory. The area has received extensive attention over four decades, but many problems remain unsolved, especially for directed graphs. A directed graph is 2-edge-connected…

We present two algorithms for maintaining the topological order of a directed acyclic graph with n vertices, under an online edge insertion sequence of m edges. Efficient algorithms for online topological ordering have many applications,…

Computing the winning set for B{\"u}chi objectives in alternating games on graphs is a central problem in computer aided verification with a large number of applications. The long standing best known upper bound for solving the problem is…

Many applications require randomly sampling bipartite graphs with fixed degrees, or randomly sampling incidence matrices with fixed row and column sums. Although several sampling algorithms exist, the ``curveball'' algorithm is the most…

We prove that in an n-vertex graph, induced chordal and interval subgraphs with the maximum number of vertices can be found in time $O(2^{\lambda n})$ for some $\lambda<1$. These are the first algorithms breaking the trivial $2^n n^{O(1)}$…

In this paper we propose an online approximate k-nn graph building algorithm, which is able to quickly update a k-nn graph using a flow of data points. One very important step of the algorithm consists in using the current distributed graph…

In the vertex cover problem, the input is a graph $G$ and an integer $k$, and the goal is to decide whether there is a set of vertices $S$ of size at most $k$ such that every edge of $G$ is incident on at least one vertex in $S$. We study…

In this paper we show an O(n^(3/2) log^2 n) time algorithm for finding a maximum flow in a planar graph with multiple sources and multiple sinks. This is the fastest algorithm whose running time depends only on the number of vertices in the…

In this paper, we present an improved algorithm for the All Pairs Non-decreasing Paths (APNP) problem on weighted simple digraphs, which has running time $\tilde{O}(n^{\frac{3 + \omega}{2}}) = \tilde{O}(n^{2.686})$. Here $n$ is the number…

In the Set Cover problem, the input is a ground set of $n$ elements and a collection of $m$ sets, and the goal is to find the smallest sub-collection of sets whose union is the entire ground set. The fastest algorithm known runs in time…

The family of $(k,\ell)$-sparse graphs, introduced by Lorea, plays a central role in combinatorial optimization and has a wide range of applications, particularly in rigidity theory. A key algorithmic problem is to decide whether a given…

Given an undirected $n$-vertex graph and $k$ pairs of terminal vertices $(s_1,t_1), \ldots, (s_k,t_k)$, the $k$-Disjoint Shortest Paths ($k$-DSP)-problem asks whether there are $k$ pairwise vertex-disjoint paths $P_1,\ldots, P_k$ such that…

Finding all maximal $k$-plexes on networks is a fundamental research problem in graph analysis due to many important applications, such as community detection, biological graph analysis, and so on. A $k$-plex is a subgraph in which every…

We present a randomized approximation algorithm for computing traveling salesperson tours in undirected regular graphs. Given an $n$-vertex, $k$-regular graph, the algorithm computes a tour of length at most $\left(1+\frac{7}{\ln…

For the constrained 2-means problem, we present a $O\left(dn+d({1\over\epsilon})^{O({1\over \epsilon})}\log n\right)$ time algorithm. It generates a collection $U$ of approximate center pairs $(c_1, c_2)$ such that one of pairs in $U$ can…