This thesis presents a comprehensive theory of information-theoretic measures for characterizing the complexity and higher-order dependence structures of graphs. We introduce multivariate complexity and dependence measures for graphs within the framework o ...
Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...
Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in an environment wi ...
In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...
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 ...
Self-attention mechanisms and non-local blocks have become crucial building blocks for state-of-the-art neural architectures thanks to their unparalleled ability in capturing long-range dependencies in the input. However their cost is quadratic with the nu ...
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
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely the data that live ...
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 ...
A motif is a frequently occurring subgraph of a given directed or undirected graph G (Milo et al.). Motifs capture higher order organizational structure of G beyond edge relationships, and, therefore, have found wide applications such as in graph clusterin ...
In several machine learning settings, the data of interest are well described by graphs. Examples include data pertaining to transportation networks or social networks. Further, biological data, such as proteins or molecules, lend themselves well to graph- ...
We show that Cutting Planes (CP) proofs are hard to find: Given an unsatisfiable formula F, It is -hard to find a CP refutation of F in time polynomial in the length of the shortest such refutation; and unless Gap-Hitting-Set admits a nontrivial algorithm, ...
Recent years have witnessed a rise in real-world data captured with rich structural information that can be better depicted by multi-relational or heterogeneous graphs.
However, research on relational representation learning has so far mostly focused on th ...
We study the computations that Bayesian agents undertake when exchanging opinions over a network. The agents act repeatedly on their private information and take myopic actions that maximize their expected utility according to a fully rational posterior be ...
This paper considers vessel scheduling with pilotage and tugging constraints in berthing operations with channel restrictions at seaports. To our knowledge, pilotage and tugging requirements have not been simultaneously considered in the literature. This w ...
In the localization game on a graph, the goal is to find a fixed but unknown target node v* with the least number of distance queries possible. In the j-th step of the game, the player queries a single node v_j and receives, as an answer to their query, th ...
Decision trees have been widely used as classifiers in many machine learning applications thanks to their lightweight and interpretable decision process. This paper introduces Tree in Tree decision graph (TnT), a framework that extends the conventional dec ...
Curran Associates, Inc, (NIPS '21: Proceedings of the 35th International Conference on Neural Information Processing Systems)2021
Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may offer new applicati ...
An integer program (IP) is a problem of the form min{f(x):Ax=b,l≤x≤u,x∈Zn}, where A∈Zm×n, b∈Zm, l,u∈Zn, and f:Zn→Z is a separable convex objective function.
The problem o ...
In this paper, we reveal an intriguing relationship between two seemingly unrelated notions: letter graphs and geometric grid classes of permutations. An important property common for both of them is well-quasi-orderability, implying, in a non-constructive ...
