In the \((1+{\varepsilon },r)\)-approximate near-neighbor problem for curves (ANNC) under some similarity measure \(\delta \), goal is to construct a data structure given set \(\mathcal {C}\) of that supports approximate queries: Given query curve Q, if there exists \(C\in \mathcal such (Q,C)\le r\), then return \(C'\in with (Q,C')\le (1+{\varepsilon })r\). There an efficient reduction from })\...

Summary The main purpose of the article is to construct a sophisticated polynomial proposed by Matiyasevich and Robinson [5] that often used reduce number unknowns in diophantine representations, using Mizar [1], [2] formalism. J k ( a <...

A quantile summary is a data structure that approximates to ε-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O( 1 ε log 1 ε ) words of memory. This improves upon the previous best upper bound of O( 1 ε log 1 ε ) by Agarwal et. ...

We study algorithms for the sliding-window model, an important variant of data-stream in which goal is to compute some function a fixed-length suffix stream. extend smooth-histogram framework Braverman and Ostrovsky (FOCS 2007) almost-smooth functions, includes all subadditive functions. Specifically, we show that if can be \(\left( 1+{{\varepsilon }}\right) \)-approximated insertion-only strea...