Most real-world optimization problems do not have an explicit problem formulation, but only allow to compute the quality of selected solution candidates. Solving such black-box optimization problems requires iterative procedures which use the feedback gained from previous evaluations to determine the strategy by which the next solution candidates are generated. Many black-box optimization algorithms, such as Simulated Annealing, Evolutionary Algorithms, Swarm Intelligence Algorithms, are randomized – making it very difficult to analyze their performances mathematically.

In the last 15 years, the theory of randomized black-box optimization has advanced considerably, and has contributed to efficient optimization by providing insights into the working principles of black-box optimization which are hard or impossible to obtain by empirical means. On the other hand, empirically-guided benchmarking has opened up new research directions for theoretical investigations.

In this presentation we will discuss the state of the art in the theory of randomized black-box optimization algorithms. As part of this critical survey we will also mention a number of open questions and connections to other fields of Computer Science.

In the literature, two kinds of process crashes are usually considered: initially dead processes and “classical” crash failures (that can occur at any time). A new notion of process failure explicitly related to contention has recently been introduced by Gadi Taubenfeld (NETYS 2018). More precisely, given a predefined contention threshold λ, this notion considers the execution in which process crashes are restricted to occur only when process contention is smaller than or equal to λ. If crashes occur after contention bypassed λ, there are no correctness guarantees. It was shown that, when λ = n-1, consensus can be solved in an n-process asynchronous read/write system despite the crash of one process, thereby circumventing the well-known FLP impossibility result.

In this talk, I will present k-set agreement and renaming algorithms that are resilient to two types of process crash failures: “λ-constrained” crash failures (as previously defined) and classical crash failures.

Learning on graphs requires a graph feature representation able to discriminate among different graphs while being amenable to fast computation. The graph isomorphism problem tells us that no fast representation of graphs is known if we require the representation to be both invariant to nodes permutation and able to discriminate two non-isomorphic graphs. Most graph representations explored so far require to be invariant. We explore new graph representations by relaxing this constraint. We present a generic embedding of graphs relying on spectral graph theory called Spectral Graph Embedding (SGE). We show that for a large family of graphs, our embedding is still invariant. To evaluate the quality and utility of our SGE, we apply them to the graph classification problem. Through extensive experiments, we show that a simple Random Forest based classification algorithm driven with our SGE reaches the state-of-the-art methods.

Although our SGE is handcrafted, we also show how our generic embedding technique can be learned and built in a data-driven manner opening the way to new learning algorithms and deep learning architectures with some invariant constraints built-in.

In Graph Theory, a reconfiguration problem is as following: given two solutions of a problem and a transition definition, is there a path of acceptable solutions from the first to the second using a transition one after another? What is the length of the shortest reconfiguration path? What complexities are involved?

For example, a recoloration problem asks if we can go from a coloration to another, by changing the color of a node at each transition (with the coloring still valid in the intermediate steps).

In this talk, the goal is to consider distributed version of two reconfiguration problems: recoloring, and reconfiguring independent sets. To parallelise the process, we will accept to change the state of different nodes at once, under certain hypothesis (for example, we will recolor an independent set of nodes). The questions will be, using the LOCAL model, how much communication is needed (i.e. how much a node needs knowledge of its neighborhood) in order to produce a reconfiguration schedule of a given length.

For the distributed recoloring, we prove that the addition of colors for the intermediate steps is needed for some cases in order to have a solution. I will provide the analysis of trees and toroidal grids, where we want to go from a 3-coloring to another with the use of a 4th color. In the case of trees, a constant schedule can be found after O(log n) communications. In the case of grids, a linear number of communications is necessary.

For the reconfiguration of independent sets, we will present different transitions from the centralized settings, to then justify the one we use. We prove that a constant schedule can be found after O(log*n) communications, and a linear schedule can be found after a constant number of communications.

Those works are the result of collaborations with Marthe Bonamy, Keren Censor-Hillel, Paul Ouvrard, Jara Uitto and Jukka Suomela

This talk concerns the problem of quickly computing distances and shortest paths on distributed networks (the CONGEST model). There have been many developments for this problem in the last few year, resulting in tight approximation schemes. This left open whether exact algorithms can perform equally well. In this talk, we will discuss some recent progress in answering this question. Most recent works that this talk is based on are with Sebastian Krinninger (FOCS 2018) and Aaron Bernstein (ArXiv 2018). Graphes

A well-known problem for which it is difficult to improve the textbook algorithm is computing the graph diameter. We present two versions of a simple algorithm (one being Monte Carlo and the other deterministic) that for every fixed $h$ and unweighted undirected graph $G$ with $n$ vertices and $m$ edges, either correctly concludes that $diam(G) < hn$ or outputs $diam(G)$, in time ${\cal O}(m+n^{1+o(1)})$. The algorithm combines a simple randomized strategy for this problem (Damaschke, {\it IWOCA'16}) with a popular framework for computing graph distances that is based on range trees (Cabello and Knauer, {\it Computational Geometry'09}). We also prove that under the Strong Exponential Time Hypothesis (SETH), we cannot compute the diameter of a given $n$-vertex graph in truly subquadratic time, even if the diameter is an $\Theta(n/\log{n})$.