SODA

We introduce a new variant of the nearest neighbor search problem, which allows for some coordinates of the dataset to be arbitrarily corrupted or unknown. Formally, given a dataset of n points P = {x₁, . . . , x_n} in high-dimensions, and a parameter k, ...

The construction of r-nets offers a powerful tool in computational and metric geometry. We focus on high-dimensional spaces and present a new randomized algorithm which efficiently computes approximate r-nets with respect to Euclidean distance. For any ...

We present a framework for similarity search based on Locality-Sensitive Filtering (LSF), generalizing the Indyk-Motwani (STOC 1998) Locality-Sensitive Hashing (LSH) framework to support space-time tradeoffs. Given a family of filters, defined as a ...

We show tight upper and lower bounds for time-space trade-offs for the c-approximate Near Neighbor Search problem. For the d-dimensional Euclidean space and n-point datasets, we develop a data structure with space n^1+ρ_u+o(1) + O(dn) and query time n^ρ_q+o(...

We analyze LSH Forest [BCG05]---a popular heuristic for the nearest neighbor search---and show that a careful yet simple modification of it outperforms "vanilla" LSH algorithms. The end result is the first instance of a simple, practical algorithm that ...

An important question in theoretical computer science is to determine the best possible running time for solving a problem at hand. For geometric optimization problems, we often understand their complexity on a rough scale, but not very well on a finer ...

In the classic circle packing problem, one asks whether a given set of circles can be packed into the unit square. This problem is known to be NP-hard. In this paper, we present a new sufficient condition using only the circles' combined area: It is ...

Solving geometric optimization problems over uncertain data has become increasingly important in many applications and has attracted a lot of attentions in recent years. In this paper, we study two important geometric optimization problems, the k-center ...

We provide simple and fast polynomial-time approximation schemes (PTASs) for several variants of the max-sum diversification problem which, in its most basic form, is as follows: given n points p₁, . . . , p_n ∈ ℝ^q and an integer k, select k points such ...

We study the problem of finding a tour of n points in which every edge is long. More precisely, we wish to find a tour that visits every point exactly once, maximizing the length of the shortest edge in the tour. The problem is known as Maximum Scatter ...

We study an iterative matrix conditioning algorithm due to Osborne (1960). The goal of the algorithm is to convert a square matrix into a balanced matrix where every row and corresponding column have the same norm. The original algorithm was proposed ...

The main result of this paper is the decidability of the membership problem for 2 × 2 nonsingular integer matrices. Namely, we will construct the first algorithm that for any nonsingular 2 × 2 integer matrices M₁, . . . , M_n and M decides whether M ...

In this paper, we show that the problem of determining if the identity matrix belongs to a finitely generated semigroup of 2 × 2 matrices from the modular group PSL₂(ℤ) and thus the Special Linear group SL₂(ℤ) is solvable in NP. From this fact, we can ...

Consider a small number of scouts exploring the infinite d-dimensional grid with the aim of hitting a hidden target point. Each scout is controlled by a probabilistic finite automaton that determines its movement (to a neighboring grid point) based on ...

We show how to design a universal shape replicator in a self-assembly system with both attractive and repulsive forces. More precisely, we show that there is a universal set of constant-size objects that, when added to any unknown hole-free polyomino ...

We present a data structure for spherical range reporting on a point set S, i.e., reporting all points in S that lie within radius r of a given query point q (with a small probability of error). Our solution builds upon the Locality-Sensitive Hashing (...

A Bloom filter is a widely used data-structure for representing a set S and answering queries of the form "Is x in S?". By allowing some false positive answers (saying 'yes' when the answer is in fact 'no') Bloom filters use space significantly below ...

In the polytope membership problem, a convex polytope K in ℝ^d is given, and the objective is to preprocess K into a data structure so that, given a query point q ∈ ℝ^d, it is possible to determine efficiently whether q ∈ K. We consider this problem in an ...

We study distributed protocols for finding all pairs of similar vectors in a large dataset. Our results pertain to a variety of discrete metrics, and we give concrete instantiations for Hamming distance. In particular, we give improved upper bounds on ...

The main result of this paper is a generalization of the classical blossom algorithm for finding perfect matchings. Our algorithm can efficiently solve Boolean CSPs where each variable appears in exactly two constraints (we call it edge CSP) and all ...

In recent years, we have seen several approaches to the graph isomorphism problem based on "generic" mathematical programming or algebraic (Gröbner basis) techniques. For most of these, lower bounds have been established. In fact, it has been shown that ...

An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a fixed domain to the variables so that all constraints are satisfied. In the ...

Given a constraint satisfaction problem (CSP) on n variables, x₁, x₂, . . . , x_n ∈ {±1}, and m constraints, a global cardinality constraint has the form of Σⁿ_{i = 1} x_i = (1 − 2p)n, where p ∈ (Ω(1), 1 − Ω(1)) and pn is an integer. Let AV G be the expected ...

Permutation Pattern Matching (or PPM) is a decision problem whose input is a pair of permutations π and τ, represented as sequences of integers, and the task is to determine whether τ contains a subsequence order-isomorphic to π. Bose, Buss and Lubiw ...

The fields of succinct data structures and compressed text indexing have seen quite a bit of progress over the last two decades. An important achievement, primarily using techniques based on the Burrows-Wheeler Transform (BWT), was obtaining the full ...

We show that the compressed suffix array and the compressed suffix tree of a string T can be built in O(n) deterministic time using O(n log σ) bits of space, where n is the string length and σ is the alphabet size. Previously described deterministic ...

Suffix tree (and the closely related suffix array) are fundamental structures capturing all substrings of a given text essentially by storing all its suffixes in the lexicographical order. In some applications, such as sparse text indexing, we work with ...

We revisit the classic problem of dynamically maintaining shortest paths between all pairs of nodes of a directed weighted graph. The allowed updates are insertions and deletions of nodes and their incident edges. We give worst-case guarantees on the ...

In this paper we consider the decremental single-source shortest paths (SSSP) problem, where given a graph G and a source node s the goal is to maintain shortest paths between s and all other nodes in G under a sequence of online adversarial edge ...

We consider the problem of maintaining an approximately maximum (fractional) matching and an approximately minimum vertex cover in a dynamic graph. Starting with the seminal paper by Onak and Rubinfeld [STOC 2010], this problem has received significant ...