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We present a new distributed} model of probabilistically checkable proofs (PCP). A satisfying assignment x ∊ \{0,1\}^n to a CNF formula \phi is shared between two parties, where Alice knows x_1, \dots, x_{n/2, Bob knows x_{n/2+1},\dots,x_n, and both parties know \phi. The goal is to have Alice and Bob jointly write a PCP that x satisfies \phi, while exchanging little or no information....
Can we analyze data without decompressing it? As our data keeps growing, understanding the time complexity of problems on compressed inputs, rather than in convenient uncompressed forms, becomes more and more relevant. Suppose we are given a compression of size n of data that originally has size N, and we want to solve a problem with time complexity T(⋅). The naïve strategy of...
The dynamic shortest paths problem on planar graphs asks us to preprocess a planar graph G such that we may support insertions and deletions of edges in G as well as distance queries between any two nodes u, v subject to the constraint that the graph remains planar at all times. This problem has been extensively studied in both the theory and experimental communities over the past decades. The best...
The CFG recognition problem is: given a context-free grammar G and a string w of length n, decide if w can be obtained from G. This is the most basic parsing question and is a core computer science problem. Valiant's parser from 1975 solves the problem in O(nO) time, where ? < 2:373 is the matrix multiplication exponent. Dozens of parsing algorithms have been proposed over the years, yet Valiant's...
Two important similarity measures between sequences are the longest common subsequence (LCS) and the dynamic time warping distance (DTWD). The computations of these measures for two given sequences are central tasks in a variety of applications. Simple dynamic programming algorithms solve these tasks in O(n2) time, and despite an extensive amount of research, no algorithms with significantly better...
We consider several well-studied problems in dynamic algorithms and prove that sufficient progress on any of them would imply a breakthrough on one of five major open problems in the theory of algorithms: 1) Is the 3SUM problem on n numbers in O(n2 -- &epsi;) time for some &epsi; > 0? 2) Can one determine the satisfiability of a CNF formula on n variables and poly n clauses in O((2...
Interest in stream monitoring is shifting toward the distributed case. In many applications the data is high volume, dynamic, and distributed, making it infeasible to collect the distinct streams to a central node for processing. Often, the monitoring problem consists of determining whether the value of a global function, defined on the union of all streams, crossed a certain threshold. We wish to...
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