相关论文: A short nonalgorithmic proof of the containers the…

We give the first truly subquadratic time algorithm, with $O^*(n^{2-1/18})$ running time, for computing the diameter of an $n$-vertex unit-disk graph, resolving a central open problem in the literature. Our result is obtained as an instance…

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…

We study graphons as a non-parametric generalization of stochastic block models, and show how to obtain compactly represented estimators for sparse networks in this framework. Our algorithms and analysis go beyond previous work in several…

We develop a theory for the existence of perfect matchings in hypergraphs under quite general conditions. Informally speaking, the obstructions to perfect matchings are geometric, and are of two distinct types: 'space barriers' from convex…

We study the problem of computing a minimum $s$--$t$ cut in an unweighted, undirected graph via \emph{cut queries}. In this model, the input graph is accessed through an oracle that, given a subset of vertices $S \subseteq V$, returns the…

This dissertation investigates the geometric combinatorics of convex polytopes and connections to the behavior of the simplex method for linear programming. We focus our attention on transportation polytopes, which are sets of all tables of…

Many authors, mainly in the context of the Bin Packing Problem with Conflicts, used the random graph generator proposed in "Heuristics and lower bounds for the bin packing problem with conflicts" [M. Gendreau, G. Laporte, and F. Semet,…

The following question arises naturally in the study of graph streaming algorithms: "Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number $n$ of…

The iterative absorption method has recently led to major progress in the area of (hyper-)graph decompositions. Amongst other results, a new proof of the Existence conjecture for combinatorial designs, and some generalizations, was…

The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…

Sample compression schemes were defined by Littlestone and Warmuth (1986) as an abstraction of the structure underlying many learning algorithms. In a sample compression scheme, we are given a large sample of vertices of a fixed hypergraph…

We present a method which provides a unified framework for most stability theorems that have been proved in graph and hypergraph theory. Our main result reduces stability for a large class of hypergraph problems to the simpler question of…

We study a design framework for robust, independently verifiable, and workload-balanced distributed algorithms working on a common input. An algorithm based on the framework is essentially a distributed encoding procedure for a…

We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional…

In [1] M. Baker and S. Norine developed a theory of divisors and linear systems on graphs, and proved a Riemann-Roch Theorem for these objects (conceived as integer-valued functions on the vertices). In [2] and [3] the authors generalized…

The visibility algorithm has been recently introduced as a mapping between time series and complex networks. This procedure allows to apply methods of complex network theory for characterizing time series. In this work we present the…

A fundamental building block in any graph algorithm is a graph container - a data structure used to represent the graph. Ideally, a graph container enables efficient access to the underlying graph, has low space usage, and supports updating…

Finding connected components in a graph is a fundamental problem in graph analysis. In this work, we present a novel minimum-mapping based Contour algorithm to efficiently solve the connectivity problem. We prove that the Contour algorithm…

This paper deals with the problem of detecting non-isotropic high-dimensional geometric structure in random graphs. Namely, we study a model of a random geometric graph in which vertices correspond to points generated randomly and…

The theme of this paper is the derivation of analytic formulae for certain large combinatorial structures. The formulae are obtained via fluid limits of pure jump type Markov processes, established under simple conditions on the Laplace…