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The well-known Disjoint Paths problem is to decide if a graph contains k pairwise disjoint paths, each connecting a different terminal pair from a set of k distinct pairs. We determine, with an exception of two cases, the complexity of the…
One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…
We consider the problem of searching for a node on a labelled random graph according to a greedy algorithm that selects a route to the desired node using metric information on the graph. Motivated by peer-to-peer networks two types of…
This work introduces a novel algorithm for finding the connected components of a graph where the vertices and edges are grouped into sets defining a Set--Based Graph. The algorithm, under certain restrictions on those sets, has the…
The path packing problem is stated finding the maximum number of edge-disjoint paths between predefined pairs of nodes in an undirected multigraph. Such a multigraph together with predefined node pairs is often called a network.
Interactions in many real-world phenomena can be explained by a strong hierarchical structure. Typically, this structure or ranking is not known; instead we only have observed outcomes of the interactions, and the goal is to infer the…
We study the problem of online graph exploration on undirected graphs, where a searcher has to visit every vertex and return to the origin. Once a new vertex is visited, the searcher learns of all neighboring vertices and the connecting…
The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph (called MaxCDP) has been recently introduced in literature, motivated by applications in social network analysis. In this paper we…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
The detection of curved lanes is still challenging for autonomous driving systems. Although current cutting-edge approaches have performed well in real applications, most of them are based on strict model assumptions. Similar to other…
We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both…
Disjoint paths problems are among the most prominent problems in combinatorial optimization. The edge- as well as vertex-disjoint paths problem, are NP-complete on directed and undirected graphs. But on undirected graphs, Robertson and…
Graph Generating Dependencies (GGDs) informally express constraints between two (possibly different) graph patterns which enforce relationships on both graph's data (via property value constraints) and its structure (via topological…
Many exact search algorithms for NP-hard graph problems adopt the old Davis-Putman branch-and-reduce paradigm. The performance of these algorithms often suffers from the increasing number of graph modifications, such as vertex/edge…
In this paper we consider several problems concerning packet routing in distributed systems. Each problem is formulated using terms from Graph Theory and for each problem we present efficient, novel, algorithmic techniques for computing…
We discuss the problem of extending data mining approaches to cases in which data points arise in the form of individual graphs. Being able to find the intrinsic low-dimensionality in ensembles of graphs can be useful in a variety of…
Decompositional parameters such as treewidth are commonly used to obtain fixed-parameter algorithms for NP-hard graph problems. For problems that are W[1]-hard parameterized by treewidth, a natural alternative would be to use a suitable…
We consider the problem of placing arrow heads in directed graph drawings without them overlapping other drawn objects. This gives drawings where edge directions can be deduced unambiguously. We show hardness of the problem, present exact…
Consider a random graph model where each possible edge $e$ is present independently with some probability $p_e$. Given these probabilities, we want to build a large/heavy matching in the randomly generated graph. However, the only way we…
Traffic forecasting is important for the success of intelligent transportation systems. Deep learning models, including convolution neural networks and recurrent neural networks, have been extensively applied in traffic forecasting problems…