Related papers: Performance of a greedy algorithm for edge coverin…
In the classic online graph balancing problem, edges arrive sequentially and must be oriented immediately upon arrival, to minimize the maximum in-degree. For adversarial arrivals, the natural greedy algorithm is $O(\log n)$-competitive,…
The random greedy algorithm for finding a maximal independent set in a graph constructs a maximal independent set by inspecting the graph's vertices in a random order, adding the current vertex to the independent set if it is not adjacent…
We study the graphs formed from instances of the stable matching problem by connecting pairs of elements with an edge when there exists a stable matching in which they are matched. Our results include the NP-completeness of recognizing…
This paper leverages the framework of algorithms-with-predictions to design data structures for two fundamental dynamic graph problems: incremental topological ordering and cycle detection. In these problems, the input is a directed graph…
Finding a maximum-weight matching is a classical and well-studied problem in computer science, solvable in cubic time in general graphs. We consider the specialization called assignment problem where the input is a bipartite graph, and…
There are many methods to find a maximum (or maximal) clique in large networks. Due to the nature of combinatorics, computation becomes exponentially expensive as the number of vertices in a graph increases. Thus, there is a need for…
Nearly three decades ago, Bar-Noy, Motwani and Naor showed that no online edge-coloring algorithm can edge color a graph optimally. Indeed, their work, titled "the greedy algorithm is optimal for on-line edge coloring", shows that the…
We analyze the problem of identifying large cliques in graphs that are affected by adversarial uncertainty. More specifically, we consider a new formulation, namely the adversarial maximum clique problem, which extends the classical…
We propose a new greedy algorithm for the maximum cardinality matching problem. We give experimental evidence that this algorithm is likely to find a maximum matching in random graphs with constant expected degree c>0, independent of the…
Finding maximum cliques in large networks is a challenging combinatorial problem with many real-world applications. We present a fast algorithm to achieve the exact solution for the maximum clique problem in large sparse networks based on…
We consider the constrained graph alignment problem which has applications in biological network analysis. Given two input graphs $G_1=(V_1,E_1), G_2=(V_2,E_2)$, a pair of vertex mappings induces an {\it edge conservation} if the vertex…
A canonical problem in graph mining is the detection of dense communities. This problem is exacerbated for a graph with a large order and size -- the number of vertices and edges -- as many community detection algorithms scale poorly. In…
In the {\sc Cluster Deletion} problem the goal is to remove the minimum number of edges of a given graph, such that every connected component of the resulting graph constitutes a clique. It is known that the decision version of {\sc Cluster…
Temporal graphs have been recently introduced to model changes to a given network that occur throughout a fixed period of time. The Temporal $\Delta$ Clique problem, that generalizes the well known Clique problem to temporal graphs, has…
When searching for characteristic subpatterns in potentially noisy graph data, it appears self-evident that having multiple observations would be better than having just one. However, it turns out that the inconsistencies introduced when…
In this work we consider temporal graphs, i.e. graphs, each edge of which is assigned a set of discrete time-labels drawn from a set of integers. The labels of an edge indicate the discrete moments in time at which the edge is available. We…
We consider the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges. We present nearly tight bounds on the magnitude of change in the set of maximal cliques, as well as…
The monography presents a new algorithm for finding the clique of maximal length in a nonseparable graph. The algorithm is based on the properties of the representation of a clique as a subset of the set of cycles with a length of three,…
A geometric intersection graph is constructed over a set of geometric objects, where each vertex represents a distinct object and an edge connects two vertices if and only if the corresponding objects intersect. We examine the problem of…
State of the art maximum clique algorithms use a greedy graph colouring as a bound. We show that greedy graph colouring can be misleading, which has implications for parallel branch and bound.