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In a previous version of this document we misinterpreted the runtime of a part of the described algorithm. Indeed, the runtime is not better than the Grover-Algorithm. We therefor withdraw this work. We present a novel algorithmic approach…
The theory of grey systems plays an important role in science,engineering and in the everyday life in general for handling approximate data. In the present paper grey numbers are used as a tool for assessing with linguistic expressions the…
Non-deterministic measurements are common in real-world scenarios: the performance of a stochastic optimization algorithm or the total reward of a reinforcement learning agent in a chaotic environment are just two examples in which…
We study the coloring problem: Given a graph G, decide whether $c(G) \leq q$ or $c(G) \ge Q$, where c(G) is the chromatic number of G. We derive conditional hardness for this problem for any constant $3 \le q < Q$. For $q\ge 4$, our result…
We study colored coverage and clustering problems. Here, we are given a colored point set where the points are covered by (unknown) $k$ clusters, which are monochromatic (i.e., all the points covered by the same cluster, have the same…
The standard two-sided and one-sided matching problems, and the closely related school choice problem, have been widely studied from an axiomatic viewpoint. A small number of algorithms dominate the literature. For two-sided matching, the…
There seems to be an upper limit to predicting the outcome of matches in (semi-)professional sports. Recent work has proposed that this is due to chance and attempts have been made to simulate the distribution of win percentages to identify…
The problem of sampling edge-colorings of graphs with maximum degree $\Delta$ has received considerable attention and efficient algorithms are available when the number of colors is large enough with respect to $\Delta$. Vizing's theorem…
A central problem in multiagent systems is the fair assignment of objects to agents. In this paper, we initiate the analysis of classic majoritarian social choice functions in assignment. Exploiting the special structure of the assignment…
Anomaly detection in large populations is a challenging but highly relevant problem. The problem is essentially a multi-hypothesis problem, with a hypothesis for every division of the systems into normal and anomal systems. The number of…
We begin by reviewing some probabilistic results about the Dirichlet Process and its close relatives, focussing on their implications for statistical modelling and analysis. We then introduce a class of simple mixture models in which…
An important area of combinatorial optimization is the study of packing and covering problems, such as Bin Packing, Multiple Knapsack, and Bin Covering. Those problems have been studied extensively from the viewpoint of approximation…
In an election in which each voter ranks all of the candidates, we consider the head-to-head results between each pair of candidates and form a labeled directed graph, called the margin graph, which contains the margin of victory of each…
In many real world situations, collective decisions are made using voting. Moreover, scenarios such as committee or board elections require voting rules that return multiple winners. In multi-winner approval voting (AV), an agent may vote…
In real-world applications, users often favor structurally diverse design choices over one high-quality solution. It is hence important to consider more solutions that decision makers can compare and further explore based on additional…
When randomized ensembles such as bagging or random forests are used for binary classification, the prediction error of the ensemble tends to decrease and stabilize as the number of classifiers increases. However, the precise relationship…
Random constraint satisfaction problems can exhibit a phase where the number of constraints per variable $\alpha$ makes the system solvable in theory on the one hand, but also makes the search for a solution hard, meaning that common…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
Polyak momentum (PM), also known as the heavy-ball method, is a widely used optimization method that enjoys an asymptotic optimal worst-case complexity on quadratic objectives. However, its remarkable empirical success is not fully…