Related papers: Correspondence Between Two Antimatroid Algorithmic…
We consider three forms of composition of matroids, each of which extends the category of bimatroids to a rigid monoidal category. Many well-known constructions are functorial or defined by morphisms in these categories. Motivating examples…
In a simple model of assigning workers to tasks, every solution that minimizes the load difference between the most loaded worker and the least loaded one actually minimizes the maximal load and maximizes the minimal load. This can be seen…
The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected…
Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects…
In this paper we provide two recognition algorithms for the class of signed-graphic matroids along with necessary and sufficient conditions for a matroid to be signed-graphic. Specifically, we provide a polynomial-time algorithm which…
Stochastic orders are very useful tool to compare the lifetimes of two coherent systems. We show that, under certain conditions, a coherent system of used components performs better (worse) than a used coherent system with respect to…
We consider whether given a simple, finite description of a group in the form of an algorithm, it is possible to algorithmically determine if the corresponding group has some specified property or not. When there is such an algorithm, we…
By the growing trend of online shopping and e-commerce websites, recommendation systems have gained more importance in recent years in order to increase the sales ratios of companies. Different algorithms on recommendation systems are used…
Efficient deterministic algorithms to construct representations of lattice path matroids over finite fields are presented. They are built on known constructions of hierarchical secret sharing schemes, a recent characterization of…
In this article, we investigate the multi-parametric matroid problem. The weights of the elements of the matroid's ground set depend linearly on an arbitrary but fixed number of parameters, each of which is taken from a real interval. The…
We present an algebraic framework which simultaneously generalizes the notion of linear subspaces, matroids, valuated matroids, and oriented matroids. We call the resulting objects matroids over hyperfields. In fact, there are (at least)…
Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…
Poetry and prose are written artistic expressions that help us to appreciate the reality we live. Each of these styles has its own set of subjective properties, such as rhyme and rhythm, which are easily caught by a human reader's eye and…
Algorithmic fairness is a new interdisciplinary field of study focused on how to measure whether a process, or algorithm, may unintentionally produce unfair outcomes, as well as whether or how the potential unfairness of such processes can…
We define an algorithm to be the set of programs that implement or express that algorithm. The set of all programs is partitioned into equivalence classes. Two programs are equivalent if they are essentially the same program. The set of…
In this paper, we present a lattice-theoretic characterization for valuated matroids, which is an extension of the well-known cryptomorphic equivalence between matroids and geometric lattices ($=$ atomistic semimodular lattices). We…
In a totally ordered set the notion of sorting a finite sequence is defined through a suitable permutation of the sequence's indices. In this paper we prove a simple formula that explicitly describes how the elements of a sequence are…
The possible impact of algorithmic recommendation on the autonomy and free choice of Internet users is being increasingly discussed, especially in terms of the rendering of information and the structuring of interactions. This paper aims at…
We study a subclass of POMDPs, called Deterministic POMDPs, that is characterized by deterministic actions and observations. These models do not provide the same generality of POMDPs yet they capture a number of interesting and challenging…
Polymatroids can be considered as "fractional matroid" where the rank function is not required to be integer valued. Many, but not every notion in matroid terminology translates naturally to polymatroids. Defining cyclic flats of a…