We consider the problem of sampling from a distribution on graphs, specifically when the distribution is defined by an evolving graph model, and consider the time, space, and randomness complexities of such samplers.
In the standard approach, the whole ...
Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For this reason, ...
This article proves strong lower bounds for distributed computing in the congest model, by presenting the bit-gadget: a new technique for constructing graphs with small cuts.
The contribution of bit-gadgets is twofold. First, developing careful sparse ...
We consider algorithms with access to an unknown matrix M ε F n×d via matrix-vector products, namely, the algorithm chooses vectors v1, ⃛ , vq, and observes Mv1, ⃛ , Mvq. Here the vi can be randomized as well as chosen adaptively as a function of Mv1, ⃛ , ...
Given an ideal I and a polynomial f the Ideal Membership Problem (IMP) is to test if f ϵ I. This problem is a fundamental algorithmic problem with important applications and notoriously intractable.
We study the complexity of the IMP for combinatorial ...
We study the two-dimensional geometric knapsack problem, in which we are given a set of n axis-aligned rectangular items, each one with an associated profit, and an axis-aligned square knapsack. The goal is to find a (non-overlapping) packing of a maximum ...
We introduce the zip tree,1 a form of randomized binary search tree that integrates previous ideas into one practical, performant, and pleasant-to-implement package. A zip tree is a binary search tree in which each node has a numeric rank and the tree is (...
We present the first nontrivial approximation algorithm for the bottleneck asymmetric traveling salesman problem. Given an asymmetric metric cost between n vertices, the problem is to find a Hamiltonian cycle that minimizes its bottleneck (or maximum-...
We study two popular ways to sketch the shortest path distances of an input graph. The first is distance preservers, which are sparse subgraphs that agree with the distances of the original graph on a given set of demand pairs. Prior work on distance ...