In this thesis we design online combinatorial optimization algorithms for beyond worst-case analysis settings.In the first part, we discuss the online matching problem and prove that, in the edge arrival model, no online algorithm can achieve a competiti ...
Graph machine learning offers a powerful framework with natural applications in scientific fields such as chemistry, biology and material sciences.
By representing data as a graph, we encode the prior knowledge that the data is composed of a set of entiti ...
An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n.
Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...
With the increasing prevalence of massive datasets, it becomes important to design algorithmic techniques for dealing with scenarios where the input to be processed does not fit in the memory of a single machine. Many highly successful approaches have emer ...
We solve the Bin Packing problem in O^*(2^k) time, where k is the number of items less or equal to one third of the bin capacity. This parameter measures the distance from the polynomially solvable case of only large (i.e., greater than one third) items. O ...
Schloss Dagstuhl – Leibniz-Zentrum fur Informatik2022
Submodular functions are a widely studied topic in theoretical computer science. They have found several applications both theoretical and practical in the fields of economics, combinatorial optimization and machine learning. More recently, there have also ...
Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...
Graph sparsification has been studied extensively over the past two decades, culminating in spectral sparsifiers of optimal size (up to constant factors). Spectral hypergraph sparsification is a natural analogue of this problem, for which optimal bounds on ...
We approach the graph generation problem from a spectral perspective by first generating the dominant parts of the graph Laplacian spectrum and then building a graph matching these eigenvalues and eigenvectors. Spectral conditioning allows for direct model ...
A plethora of real world problems consist of a number of agents that interact, learn, cooperate, coordinate, and compete with others in ever more complex environments. Examples include autonomous vehicles, robotic agents, intelligent infrastructure, IoT de ...
