Related papers: Access Structures Determined by Uniform Polymatroi…
Traditional threshold secret sharing cannot realizing all access structures of secret sharing. So, Ito introduced the concept of Secret sharing scheme realizing general access structure. But Its scheme has to send multiple shares to each…
Disjunctive Hierarchical Secret Sharing (DHSS) scheme is a secret sharing scheme in which the set of all participants is partitioned into disjoint subsets. Each disjoint subset is said to be a level, and different levels have different…
In an on-line secret sharing scheme the dealer assigns shares in the order the participants show up, knowing only those qualified subsets whose all members she has seen. We assume that the overall access structure is known and only the…
Every bi-uniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given…
Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence…
This work introduces a new class of symmetric matrix structures, called harmonic structures, which enable the generation of all possible directed transitions $(x_i, x_{i+1})$ over a set of $n$ symbols, without internal repetitions. Unlike…
Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered.…
We consider matroid allocation problems under opportunity fairness constraints: resources need to be allocated to a set of agents under matroid constraints (which include classical problems such as bipartite matching). Agents are divided…
Sharing a secret efficiently amongst a group of participants is not easy since there is always an adversary / eavesdropper trying to retrieve the secret. In secret sharing schemes, every participant is given a unique share. When the desired…
Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set…
We introduce the notion of a quasi-matroidal class of ordered simplicial complexes: an approximation to the idea of a matroid cryptomorphism in the landscape of ordered simplicial complexes. A quasi-matroidal class contains pure shifted…
The Matroid Secretary Problem (MSP) is one of the most prominent settings for online resource allocation and optimal stopping. A decision-maker is presented with a ground set of elements $E$ revealed sequentially and in random order. Upon…
A new connection between two different necessary conditions for a polymatroid to be linearly representable is presented. Specifically, we prove that the existence of a tensor product with the uniform matroid of rank two on three elements…
In this paper, we consider the case that sharing many secrets among a set of participants using the threshold schemes. All secrets are assumed to be statistically independent and the weak secure condition is focused on. Under such…
Maintaining a maximum bipartite matching online while minimizing recourse/augmentations is a well studied problem, motivated by content delivery, job scheduling, and hashing. A breakthrough result of Bernstein, Holm, and Rotenberg…
The secretary problem became one of the most prominent online selection problems due to its numerous applications in online mechanism design. The task is to select a maximum weight subset of elements subject to given constraints, where…
At present, practical application and theoretical discussion of rough sets are two hot problems in computer science. The core concepts of rough set theory are upper and lower approximation operators based on equivalence relations. Matroid,…
Multiparty session types (MST) are a well-established type theory that describes the interactive structure of a fixed number of components from a global point of view and type-checks the components through projection of the global type onto…
An important parameter in a secret sharing scheme is the number of minimal qualified sets. Given this number, the universal access structure is the richest possible structure, namely the one in which there are one or more participants in…
We combine some known results and techniques with new ones to show that there exists a non-algebraic, multi-linear matroid. This answers an open question by Matus (Discrete Mathematics 1999), and an open question by Pendavingh and van Zwam…