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Graphs are a natural representation of data from various contexts, such as social connections, the web, road networks, and many more. In the last decades, many of these networks have become enormous, requiring efficient algorithms to cut…
Temporal graphs represent interactions between entities over time. These interactions may be direct, a contact between two vertices at some time instant, or indirect, through sequences of contacts called journeys. Deciding whether an entity…
In the constraint programming framework, state-of-the-art static and dynamic decomposition techniques are hard to apply to problems with complete initial constraint graphs. For such problems, we propose a hybrid approach of these techniques…
A hypergraph is a set V of vertices and a set of non-empty subsets of V, called hyperedges. Unlike graphs, hypergraphs can capture higher-order interactions in social and communication networks that go beyond a simple union of pairwise…
Partial graph matching extends traditional graph matching by allowing some nodes to remain unmatched, enabling applications in more complex scenarios. However, this flexibility introduces additional complexity, as both the subset of nodes…
The basic (and traditional) crossing number problem is to determine the minimum number of crossings in a topological drawing of an input graph in the plane. We develop a unified framework yielding fixed-parameter tractable (FPT) algorithms…
Highly dynamic networks rarely offer end-to-end connectivity at a given time. Yet, connectivity in these networks can be established over time and space, based on temporal analogues of multi-hop paths (also called {\em journeys}).…
The functional demands of robotic systems often require completing various tasks or behaviors under the effect of disturbances or uncertain environments. Of increasing interest is the autonomy for dynamic robots, such as multirotors, motor…
We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis…
The classic technique of Baker [J. ACM '94] is the most fundamental approach for designing approximation schemes on planar, or more generally topologically-constrained graphs, and it has been applied in a myriad of different variants and…
We study the problem of maintaining a breadth-first spanning tree and the induced BFS ordering in a directed graph under edge updates. While semi-dynamic algorithms are known, maintaining the spanning tree, level information, and numbering…
The number of multi-robot systems deployed in field applications has increased dramatically over the years. Despite the recent advancement of navigation algorithms, autonomous robots often encounter challenging situations where the control…
We give new partially-dynamic algorithms for the all-pairs shortest paths problem in weighted directed graphs. Most importantly, we give a new deterministic incremental algorithm for the problem that handles updates in…
We initiate the study of graph algorithms in the streaming setting on massive distributed and parallel systems inspired by practical data processing systems. The objective is to design algorithms that can efficiently process evolving graphs…
In this paper we introduce a new network reachability problem where the goal is to find the most reliable path between two nodes in a network, represented as a directed acyclic graph. Individual edges within this network may fail according…
Distributed processing of large-scale graph data has many practical applications and has been widely studied. In recent years, a lot of distributed graph processing frameworks and algorithms have been proposed. While many efforts have been…
Given a large graph, the densest-subgraph problem asks to find a subgraph with maximum average degree. When considering the top-$k$ version of this problem, a na\"ive solution is to iteratively find the densest subgraph and remove it in…
This paper will analyze several quadratic-time solvable problems, and will classify them into two classes: problems that are solvable in truly subquadratic time (that is, in time $O(n^{2-\epsilon})$ for some $\epsilon>0$) and problems that…
In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning…
We consider the all pairs all shortest paths (APASP) problem, which maintains all of the multiple shortest paths for every vertex pair in a directed graph $G=(V,E)$ with a positive real weight on each edge. We present two fully dynamic…