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We describe algorithms to efficiently compute minimum $(s,t)$-cuts and global minimum cuts of undirected surface-embedded graphs. Given an edge-weighted undirected graph $G$ with $n$ vertices embedded on an orientable surface of genus $g$,…
A flow graph $G=(V,E,s)$ is a directed graph with a distinguished start vertex $s$. The dominator tree $D$ of $G$ is a tree rooted at $s$, such that a vertex $v$ is an ancestor of a vertex $w$ if and only if all paths from $s$ to $w$…
On an evolving graph that is continuously updated by a high-velocity stream of edges, how can one efficiently maintain if two vertices are connected? This is the connectivity problem, a fundamental and widely studied problem on graphs. We…
In this paper we investigate the computational complexity of learning the graph structure underlying a discrete undirected graphical model from i.i.d. samples. We first observe that the notoriously difficult problem of learning parities…
The problem of matching a query string to a directed graph, whose vertices are labeled by strings, has application in different fields, from data mining to computational biology. Several variants of the problem have been considered,…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
In this paper, motivated by a question posed in \cite{AH}, we introduce strongly biconvex graphs as a subclass of weakly chordal and bipartite graphs. We give a linear time algorithm to find an induced matching for such graphs and we prove…
We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…
Graph pattern matching is a routine process for a wide variety of applications such as social network analysis. It is typically defined in terms of subgraph isomorphism which is NP-Complete. To lower its complexity, many extensions of graph…
Graph processing is used extensively in areas from social networking mining to web indexing. We demonstrate that the performance and dependability of such applications critically hinges on the graph data structure used, because a fixed,…
We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph.…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
We investigate the parameterized complexity of the graph editing problem called Editing to a Graph with a Given Degree Sequence, where the aim is to obtain a graph with a given degree sequence \sigma by at most k vertex or edge deletions…
A "genome structure" is a labeled directed graph with vertices of degree 1 or 2. A set of operations over such graphs is fixed, and each of the operations has a certain cost, a strictly positive number. The transformation problem consists…
Graph embedding provides an efficient solution for graph analysis by converting the graph into a low-dimensional space which preserves the structure information. In contrast to the graph structure data, the i.i.d. node embedding can be…
A strength of parameterized algorithmics is that each problem can be parameterized by an essentially inexhaustible set of parameters. Usually, the choice of the considered parameter is informed by the theoretical relations between…
In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…
We consider the problem of transforming a given graph $G_s$ into a desired graph $G_t$ by applying a minimum number primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each…
The computation of distance measures between nodes in graphs is inefficient and does not scale to large graphs. We explore dense vector representations as an effective way to approximate the same information: we introduce a simple yet…
We train an agent to navigate in 3D environments using a hierarchical strategy including a high-level graph based planner and a local policy. Our main contribution is a data driven learning based approach for planning under uncertainty in…