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Many optimization problems can be naturally represented as (hyper) graphs, where vertices correspond to variables and edges to tasks, whose cost depends on the values of the adjacent variables. Capitalizing on the structure of the graph,…
Given a graph of which the n vertices form a regular two-dimensional grid, and in which each (possibly weighted and/or directed) edge connects a vertex to one of its eight neighbours, the following can be done in O(scan(n)) I/Os, provided M…
Fully dynamic graph algorithms that achieve polylogarithmic or better time per operation use either a hierarchical graph decomposition or random-rank based approach. There are so far two graph properties for which efficient algorithms for…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
We study dynamic $(1+\epsilon)$-approximation algorithms for the all-pairs shortest paths problem in unweighted undirected $n$-node $m$-edge graphs under edge deletions. The fastest algorithm for this problem is a randomized algorithm with…
Given a connected, undirected graph whose edges are labelled (or coloured), the minimum labelling spanning tree (MLST) problem seeks a spanning tree whose edges have the smallest number of distinct labels (or colours). In recent work, the…
We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case…
A number of problems in parallel computing require reasoning about the dependency structure in parallel programs. For example, dynamic race detection relies on efficient "on-the-fly" determination of dependencies between sequential and…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
The Minimum Dominating Set (MDS) problem is a well-established combinatorial optimization problem with numerous real-world applications. Its NP-hard nature makes it increasingly difficult to obtain exact solutions as the graph size grows.…
We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
Message-passing algorithms based on belief-propagation (BP) are successfully used in many applications including decoding error correcting codes and solving constraint satisfaction and inference problems. BP-based algorithms operate over…
We present a comprehensive classical and parameterized complexity analysis of decision tree pruning operations, extending recent research on the complexity of learning small decision trees. Thereby, we offer new insights into the…
In this paper we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is…
Linear diagrams are an effective way to visualize set-based data by representing elements as columns and sets as rows with one or more horizontal line segments, whose vertical overlaps with other rows indicate set intersections and their…
While operating communication networks adaptively may improve utilization and performance, frequent adjustments also introduce an algorithmic challenge: the re-optimization of traffic engineering solutions is time-consuming and may limit…
This paper presents near-optimal deterministic parallel and distributed algorithms for computing $(1+\varepsilon)$-approximate single-source shortest paths in any undirected weighted graph. On a high level, we deterministically reduce this…
We give an algorithm for finding the arboricity of a weighted, undirected graph, defined as the minimum number of spanning forests that cover all edges of the graph, in $\sqrt{n} m^{1+o(1)}$ time. This improves on the previous best bound of…
An NP-hard graph problem may be intractable for general graphs but it could be efficiently solvable using dynamic programming for graphs with bounded width (or depth or some other structural parameter). Dynamic programming is a well-known…