Stronger lower bounds for text searching and polynomial evaluation

نویسنده

  • Alexander Golynski
چکیده

In this paper, we give two main technical results: (i) we show a stronger lower bound for substring search problem via compression extending results of Demaine and López-Ortiz (SODA ’01); (ii) improve the results of Gal and Miltersen (ICALP ’03) by showing a bound on the redundancy needed by the polynomial evaluation problem that is linear in terms of the information-theoretic minimum storage required by a polynomial.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Upper and Lower Bounds for Text Upper and Lower Bounds for Text Indexing Data Structures

The main goal of this thesis is to investigate the complexity of a variety of problems related to text indexing and text searching. We present new data structures that can be used as building blocks for full-text indices which occupies minute space (FM-indexes) and wavelet trees. These data structures also can be used to represent labeled trees and posting lists. Labeled trees are applied in XM...

متن کامل

Some lower bounds for the $L$-intersection number of graphs

‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

متن کامل

TWO LOW-ORDER METHODS FOR THE NUMERICAL EVALUATION OF CAUCHY PRINCIPAL VSlLUE INTEGRALS OF OSCILLATORY KIND

In this paper, we develop two piecewise polynomial methods for the numerical evaluation of Cauchy Principal Value integrals of oscillatory kind. The two piecewisepolynomial quadratures are compact, easy to implement, and are numerically stable. Two numerical examples are presented to illustrate the two rules developed, The convergence of the two schemes is proved and some error bounds obtai...

متن کامل

A note on circuit lower bounds from derandomization

We present an alternate proof of the result by Kabanets and Impagliazzo that derandomizing polynomial identity testing implies circuit lower bounds. Our proof is simpler, scales better, and yields a somewhat stronger result than the original argument.

متن کامل

"Resistant" Polynomials and Stronger Lower Bounds for Depth-Three Arithmetical Formulas

We derive quadratic lower bounds on the ∗-complexity of sum-of-products-of-sums (ΣΠΣ) formulas for classes of polynomials f that have too few partial derivatives for the (near-)quadratic lower bound techniques of Shpilka and Wigderson [SW99, Shp01] (after [NW96]). Our techniques introduce a notion of “resistance” which connotes full-degree behavior of f under any projection to an affine space o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007