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This work seeks to tackle the inherent complexity of dataspaces by introducing a novel data structure that can represent datasets across multiple levels of abstraction, ranging from local to global. We propose the concept of a multilevel…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
We report on a recent breakthrough in rule-based graph programming, which allows us to reach the time complexity of imperative linear-time algorithms. In general, achieving the complexity of graph algorithms in conventional languages using…
The retrieval problem is the problem of associating data with keys in a set. Formally, the data structure must store a function f: U ->{0,1}^r that has specified values on the elements of a given set S, a subset of U, |S|=n, but may have…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
This paper proves the first super-logarithmic lower bounds on the cell probe complexity of dynamic boolean (a.k.a. decision) data structure problems, a long-standing milestone in data structure lower bounds. We introduce a new method for…
We introduce a novel architecture for graph networks which is equivariant to any transformation in the coordinate embeddings that preserves the distance between neighbouring nodes. In particular, it is equivariant to the Euclidean and…
With the ubiquity of large-scale graph data in a variety of application domains, querying them effectively is a challenge. In particular, reachability queries are becoming increasingly important, especially for containment, subsumption, and…
A temporal graph $G$ is a sequence $(G_t)_{t \in I}$ of graphs on the same vertex set of size $n$. The \emph{temporal exploration problem} asks for the length of the shortest sequence of vertices that starts at a given vertex, visits every…
It is known that any chordal graph on $n$ vertices can be represented as the intersection of $n$ subtrees in a tree on $n$ nodes. This fact is recently used in [2] to generate random chordal graphs on $n$ vertices by generating $n$ subtrees…
A unit disk graph is the intersection graph of n congruent disks in the plane. Dominating sets in unit disk graphs are widely studied due to their application in wireless ad-hoc networks. Because the minimum dominating set problem for unit…
A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of…
Temporal graphs are graphs where the edge set can change in each time step, and the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been…
We present the first comprehensive analysis of temporal settings for directed temporal graphs, fully resolving their hierarchy with respect to support, reachability, and induced-reachability equivalence. These notions, introduced by…
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,…
In this paper, we consider two fundamental cut approximation problems on large graphs. We prove new lower bounds for both problems that are optimal up to logarithmic factors. The first problem is to approximate cuts in balanced directed…
Motivation: Second generation sequencing technology makes it feasible for many researches to obtain enough sequence reads to attempt the de novo assembly of higher eukaryotes (including mammals). De novo assembly not only provides a tool…
Analyzing interconnection structures among underlying entities or objects in a dataset through the use of graph analytics has been shown to provide tremendous value in many application domains. However, graphs are not the primary…
The segment number of a planar graph $G$ is the smallest number of line segments needed for a planar straight-line drawing of $G$. Dujmovi\'c, Eppstein, Suderman, and Wood [CGTA'07] introduced this measure for the visual complexity of…
During the past decades significant efforts have been made to propose data structures for answering connectivity queries on fully dynamic graphs, i.e., graphs with frequent insertions and deletions of edges. However, a comprehensive…