相关论文: Some interesting problems

We introduce a novel collection of uniqueness problems, with related sampling and interpolation issues. We call them deep zero problems, as they are concerned with local properties at a small number of given points.

This paper presents a simple extension of the binary heap, the List Heap. We use List Heaps to demonstrate the idea of adaptive heaps: heaps whose performance is a function of both the size of the problem instance and the disorder of the…

This literature review covers the research and thought process that went into making a solution for the infinite scrolling problem faced in streaming services such as Netflix. Using the data collected, we have come to the conclusion that an…

We study some problems inherent with certain forms of functional depth, in particular, zero depth and lack of consistency.

Our number system is a magnificent tool. But it is far from perfect. Can it be improved? In this paper some possibilities are discussed, including the use of a different base or directed (negative as well as positive) numerals. We also put…

A collection of 50 open problems around the structure theory of ultraproducts of II$_1$ factors is presented, along with some annotations and references.

This paper discussed the {\it robust alignment} problem, that is, the problem of aligning the goals of algorithms with human preferences. It presented a general roadmap to tackle this issue. Interestingly, this roadmap identifies 5 critical…

Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.

After a brief discussion of the history of the problem, we propose a generalization of the map colouring problem to higher dimensions.

This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.

As we go along with a bioinformatic analysis we stumbled over a new combinatorial question. Although the problem is a very special one, there are maybe more applications than only this one we have. This text is mainly about the general…

Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem…

Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and…

We study an extension of the Arrival problem, called Recursive Arrival, inspired by Recursive State Machines, which allows for a family of switching graphs that can call each other in a recursive way. We study the computational complexity…

The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…

We provide an overview of some recent progress on the complexity of election systems. The issues studied include the complexity of the winner, manipulation, bribery, and control problems.

Enumeration of tilings is the mathematical study concerning the total number of coverings of regions by similar pieces without gaps or overlaps. Enumeration of tilings has become a vibrant subfield of combinatorics with connections and…

We consider the problem of enumeration of incongruent two-color bracelets of $n$ beads, $k$ of which are black, and study several natural variations of this problem. We also give recursion formulas for enumeration of $t$-color bracelets,…

In order to compare and benchmark the mathematical software, the performance profiles have been introduced [1]. However, it has been proved that the algorithm is not flawless. The main issue with the performance profile is that it may rank…

The aim of this survey article is to highlight several notoriously intractable problems about knots and links, as well as to provide a brief discussion of what is known about them.