Related papers: Neighbors
Nearest neighbor methods are a popular class of nonparametric estimators with several desirable properties, such as adaptivity to different distance scales in different regions of space. Prior work on convergence rates for nearest neighbor…
Packings of identical objects have fascinated both scientists and laymen alike for centuries, in particular the sphere packings and the packings of identical regular tetrahedra. Mathematicians have tried for centuries to determine the…
In this paper we discuss various special problems on packing and covering. Among others we survey the problems and results concerning finite arrangements, Minkowskian, saturated, compact, and totally separable packings. We discuss shortest…
The graph packing problem is a well-known area in graph theory. We consider a bipartite version and give almost tight conditions on the packability of two bipartite sequences.
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
Animals' internal states reflect variables like their position in space, orientation, decisions, and motor actions -- but how should these internal states be arranged? Internal states which frequently transition between one another should…
In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to…
The Satisfactory Partition problem consists in deciding if the set of vertices of a given undirected graph can be partitioned into two nonempty parts such that each vertex has at least as many neighbours in its part as in the other part.…
Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…
Let $G$ be a bipartite graph where every node has a strict ranking of its neighbors. For every node, its preferences over neighbors extend naturally to preferences over matchings. Matching $N$ is more popular than matching $M$ if the number…
We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which…
The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization…
We consider the problem of data exchange by a group of closely-located wireless nodes. In this problem each node holds a set of packets and needs to obtain all the packets held by other nodes. Each of the nodes can broadcast the packets in…
We introduce a two-player game in which one and his/her opponent attempt to pack as many ``prisoners'' as possible on the squares of an n-by-n checkerboard; each prisoner has to be ``protected'' by at least as many guards as the number of…
Flocking is a fascinating phenomenon observed across a wide range of living organisms. We investigate, based on a simple self-propelled particle model, how the emergence of ordered motion in a collectively moving group is influenced by the…
We start with a review of the pervasiveness of the nearest neighbor search problem and techniques used to solve it along with some experimental results. In the second chapter, we show reductions between two different classes of geo- metric…
Maximum bipartite matching is a fundamental algorithmic problem which can be solved in polynomial time. We consider a natural variant in which there is a separation constraint: the vertices on one side lie on a path or a grid, and two…
The multilayer garbage disposal game is an evolution of the garbage disposal game. Each layer represents a social relationship within a system of finitely many individuals and finitely many layers. An agent can redistribute their garbage…