SODA

The Fast Johnson-Lindenstrauss Transform (FJLT) was recently discovered by Ailon and Chazelle as a novel technique for performing fast dimension reduction with small distortion from ℓ^d₂ to ℓ^d₂ in time O(max{d log d,k³}). For k in [Ω(log d), O(d^1/2)] ...

The method of stable random projections is popular in data stream computations, data mining, information retrieval, and machine learning, for efficiently computing the lα (0 < α ≤ 2) distances using a small (memory) space, in one pass of the data.

We ...

We study the problem of estimating the best B term Fourier representation for a given frequency-sparse signal (i.e., vector) A of length N > B. More precisely, we investigate how to deterministically identify B of the largest magnitude frequencies of Â, ...

Over the recent years, a new approach for obtaining a succinct approximate representation of n-dimensional vectors (or signals) has been discovered. For any signal x, the succinct representation of x is equal to Ax, where A is a carefully chosen R x n ...

We present improved oracles for the distance sensitivity problem. The goal is to preprocess a graph G = (V,E) with non-negative edge weights to answer queries of the form: what is the length of the shortest path from x to y that does not go through some ...

Bisubmodular functions are a natural "directed", or "signed", extension of submodular functions with several applications. Recently Fujishige and Iwata showed how to extend the Iwata, Fleischer, and Fujishige (IFF) algorithm for submodular function ...

Holographic algorithms were introduced by Valiant as a new methodology to derive polynomial time algorithms. Here information and computation are represented by exponential sums using the so-called signatures. These signatures express superpositions of ...

For p ≥ 2 we consider the problem of, given an n × n matrix A = (a_ij) whose diagonal entries vanish, approximating in polynomial time the number {display equation} (where optimization is taken over real numbers).

When p = 2 this is simply the problem of ...

We study the succinct approximation of convex Pareto curves of multiobjective optimization problems. We propose the concept of ε-convex Pareto (ε-CP) set as the appropriate one for the convex setting, and observe that it can offer arbitrarily more ...

We give various deterministic polynomial time reductions among approximation problems on point lattices. Our reductions are both efficient and robust, in the sense that they preserve the rank of the lattice and approximation factor achieved. Our main ...

Given a point set P in the plane, the Delaunay graph with respect to axis-parallel rectangles is a graph defined on the vertex set P, whose two points p,q ∈ P are connected by an edge if and only if there is a rectangle parallel to the coordinate axes ...

Greedy Routing is a class of routing algorithms in which the packets are forwarded in a manner that reduces the distance to the destination at every step. In an attempt to provide theoretical guarantees for a class of greedy routing algorithms, ...

We present a method to maintain a mesh approximating a deforming surface, which is specified by a dense set of sample points. We identify a reasonable motion model for which a provably good surface mesh can be maintained. Our algorithm determines the ...

We show how to compute the planar arrangement induced by segments of arbitrary algebraic curves with the Bentley-Ottmann sweep-line algorithm. The necessary geometric primitives reduce to cylindrical algebraic decompositions of the plane for one or two ...

In the past decades the G_n,p model of random graphs, introduced by Erdős and Rényi in the 60's, has led to numerous beautiful and deep theorems. A key feature that is used in basically all proofs is that edges in G_n,p appear independently. The ...

The post-genomic era has witnessed an explosion in the quality, quantity and variety of biological data---sequence, structure, and networks. However, when building computational models on these data, some abstractions recur often. In particular, graph-...

Local Ratio is a well-known paradigm for designing approximation algorithms for combinatorial optimization problems. At a very high level, a local ratio algorithm first decomposes the input weight function w into a positive linear combination of simpler ...

We present greedy algorithms for some classes of combinatorial packing and cover problems within the general formal framework of Hoffman and Schwartz' lattice polyhedra. Our algorithms compute in a first phase Monge solutions for the associated dual ...

In this paper, we present two techniques to analyze greedy approximation with nonsubmodular functions restricted submodularity and shifted submodularity. As an application of the restricted submodularity, we present a worst-case analysis of a greedy ...

We study dense instances of MaxCut and its generalizations. Following a long list of existing, diverse and often sophisticated approximation schemes, we propose taking the naïve greedy approach; we prove that when the vertices are considered in random ...

In this paper we present algorithms for computing large matchings in 3-regular graphs, graphs with maximum degree 3, and 3-connected planar graphs. The algorithms give a guarantee on the size of the computed matching and take linear or slightly ...

The Border Gateway Protocol (BGP) is the interdomain routing protocol used to exchange routing information between Autonomous Systems (ASes) in the internet today. While intradomain routing protocols such as RIP are basically distributed algorithms for ...

We consider the problem of minimizing average latency cost while obliviously routing traffic in a network with linear latency functions. This is roughly equivalent to minimizing the function Σ_e(load(e))², where for a network link e, load(e) denotes the ...

We consider the problem of broadcasting in an unknown radio network modeled as a directed graph G = (V, E), where |V| = n. In unknown networks, every node knows only its own label, while it is unaware of any other parameter of the network, included its ...

In this paper we analyze the runtime and number of message transmissions generated by simple randomized broadcasting algorithms in random-like networks, and show that an apparently minor change in the ability of the nodes implies an exponential decrease ...

We consider the online problem of non-preemptive queue management. An online sequence of packets arrive, each of which has an associated intrinsic value. Packets can be accepted to a FIFO queue, or discarded. The profit gained by transmitting a packet ...

Gibbs sampling also known as Glauber dynamics is a popular technique for sampling high dimensional distributions defined on graphs. Of special interest is the behavior of Gibbs sampling on the Erdös-Rényi random graph G(n, d/n), where each edge is ...

We prove the following inequality on the convolution of distributions over a finite group G: {display equation} where X, Y are probability distributions over G, the * denotes convolution, U the uniform distribution over G, and || · || the l₂-norm; n is ...

We prove that binary linear concatenated codes with an outer algebraic code (specifically, a folded Reed-Solomon code) and independently and randomly chosen linear inner codes achieve the list-decoding capacity with high probability. In particular, for ...

In this paper we study noisy sorting without re-sampling. In this problem there is an unknown order {display equation} where π is a permutation on n elements. The input is the status of (ⁿ₂) queries of the form q(a_i, a_j), for i < j, where q(a_i, a_j) = + (...