Related papers: Multiple Subset Problem as an encryption scheme fo…
Formulate the problem as follows. Split a file into n pieces so that it can be restored without any m parts (1<=m<=n). Such problems are called problems secret sharing. There exists a set of methods for solving such problems, but they all…
The distributed index coding problem is studied, whereby multiple messages are stored at different servers to be broadcast to receivers with side information. First, the existing composite coding scheme is enhanced for the centralized…
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study,…
The Submodular Bin Packing (SMBP) problem asks for packing unsplittable items into a minimal number of bins for which the capacity utilization function is submodular. SMBP is equivalent to chance-constrained and robust bin packing problems…
For population studies or for the training of complex machine learning models, it is often required to gather data from different actors. In these applications, summation is an important primitive: for computing means, counts or mini-batch…
Secret sharing schemes based on the idea of hidden multipliers in encryption are proposed. As a platform, one can use both multiplicative groups of finite fields and groups of invertible elements of commutative rings, in particular,…
This article presents the use of Answer Set Programming (ASP) to mine sequential patterns. ASP is a high-level declarative logic programming paradigm for high level encoding combinatorial and optimization problem solving as well as…
Answer Set Programming (ASP) is a powerful modeling formalism for combinatorial problems. However, writing ASP models is not trivial. We propose a novel method, called Sketched Answer Set Programming (SkASP), aiming at supporting the user…
AI algorithms, and machine learning (ML) techniques in particular, are increasingly important to individuals' lives, but have caused a range of privacy concerns addressed by, e.g., the European GDPR. Using cryptographic techniques, it is…
We provide a survey on the Hidden Subgroup Problem (HSP), which plays an important role in studying the security of public-key cryptosystems. We first review the abelian case, where Kitaev's algorithm yields an efficient quantum solution to…
A sum-product network (SPN) is a graphical model that allows several types of inferences to be drawn efficiently. There are two types of learning for SPNs: Learning the architecture of the model, and learning the parameters. In this paper,…
This paper considers the problem of simultaneously communicating two messages, a high-security message and a low-security message, to a legitimate receiver, referred to as the security embedding problem. An information-theoretic formulation…
Combinatorial problems stated as Constraint Satisfaction Problems (CSP) are examined. It is shown by example that any algorithm designed for the original CSP, and involving the AllDifferent constraint, has at least the same level of…
In many real-world problems, we are dealing with collections of high-dimensional data, such as images, videos, text and web documents, DNA microarray data, and more. Often, high-dimensional data lie close to low-dimensional structures…
In this paper a secret sharing scheme based on the word problem in groups is introduced. The security of the scheme and possible variations are discussed in section 2. The article concludes with the suggestion of two categories of platform…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
We introduce the strongly NP-complete pagination problem, an extension of BIN PACKING where packing together two items may make them occupy less volume than the sum of their individual sizes. To achieve this property, an item is defined as…
This article details the algorithmics in FLSSS, an R package for solving various subset sum problems. The fundamental algorithm engages the problem via combinatorial space compression adaptive to constraints, relaxations and variations that…
The subset sum problem over finite fields is a well-known {\bf NP}-complete problem. It arises naturally from decoding generalized Reed-Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a…