Fedor Nikitin

Followers

Following

Public Views

Shmuel Tomi Klein

Bar-Ilan University

Camil Demetrescu

Università degli Studi "La Sapienza" di Roma

Shane Culpepper

RMIT University

Giulio Ermanno Pibiri

Uploads

Papers by Fedor Nikitin

Simple Compression Code Supporting Random Access and Fast String Matching

Springer eBooks, Jun 26, 2007

Given a sequence S of n symbols over some alphabet Σ, we develop a new compression method that is... more Given a sequence S of n symbols over some alphabet Σ, we develop a new compression method that is (i) very simple to implement; (ii) provides O(1) time random access to any symbol of the original sequence; (iii) allows efficient pattern matching over the compressed sequence. Our simplest solution uses at most 2h + o(h) bits of space, where h = n(H 0 (S) + 1), and H 0 (S) is the zeroth-order empirical entropy of S. We discuss a number of improvements and trade-offs over the basic method. The new method is applied to text compression. We also propose average case optimal string matching algorithms.

Download

Об общей неподвижной точке операторов значения в игре на перехват

Вестник Санкт-Петербургского университета. Серия 10. Прикладная математика. Информатика. Процессы управления, 2008

A Necessary And Sufficient Condition For The Existence Of The Value For Positional Differential Game

IFAC Proceedings Volumes, 2009

The theorem on the existence of the value for positional differential game of fixed duration is p... more The theorem on the existence of the value for positional differential game of fixed duration is presented. A necessary and sufficient condition is formulated in terms of the fixed points of value operators. This theorem supplements the theorem on the existence and uniqueness of solution for a generalized Isaacs-Bellman equation.

Simple Random Access Compression

Fundamenta Informaticae, 2009

Value operators for the control problem with disturbance

The control problem under disturbance is considered as differential game with integral-terminal t... more The control problem under disturbance is considered as differential game with integral-terminal type of payoff. For this class of games properties of value operators are studied. These operators play crucial role in non-smooth version of dynamic programming method for differential games known as programmed iteration method.

Existence and uniqueness theorem for a generalized Isaacs-Bellman equation

Differential Equations, Jun 1, 2007

Under condition (3), there exists an equilibrium in the small game for an arbitrary choice of the... more

Download

Viscosity solutions and programmed iteration method for Isaacs equation

Efficiency measurement for revenue management

Journal of Revenue and Pricing Management, May 21, 2022

Bloom filters and their applications

The bloom filters, as a new approach to hashing, were firstly presented by Burton Bloom [Blo70]. ... more The bloom filters, as a new approach to hashing, were firstly presented by Burton Bloom [Blo70]. He considered the task of presenting a set as a sequence of bits, which is called hash code of the set. In comparison with the conventional hash-coding method, author offered another technique allowing to get more concise presentation of the set, but with some errors. There are applications in which errors with some allowable level are permitted. Allowing the possibility of these errors, we can reduce a space required for presentating a set in such applications. An example is a spell-checking system where we allow some amount of mistakes in presentation of dictionary. We begin with the theory of Bloom filters. Subsection 2.1 deals with conventional hash-coding method. Firstly we introduce a hash-coding method, where no errors are permitted and then we explore how space requirements can be reduced by allowing errors in the system. In subsection 2.2 we give the definition of Bloom filter a...

Download

Efficiency measurement for revenue management

Journal of Revenue and Pricing Management

Value operators for the control problem with disturbance

2016 International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), 2016

On value operators in differential games

Applied Mathematical Sciences, 2015

In the paper basics of programmed iteration method is studied. This method appeared for the purpo... more In the paper basics of programmed iteration method is studied. This method appeared for the purposes of research of non-regular differential games. We consider zero-sum differential games with terminal payoff. We introduce value operators and prove main properties of operators used in programmed iteration method.

Download

On Regular Differential Games of Pursuit with Fixed Duration

In any differential game the programmed maxmin is a guaranteed payoff of first player. For a long... more In any differential game the programmed maxmin is a guaranteed payoff of first player. For a long time, due to the simplicity of geometric interpretation of programmed maxmin and difficulties of implementation for Isaacs' method, programmed maxmin was extensively studied. Researchers were interested in finding conditions under which programmed maxmin is the value of differential game. These conditions are called regular conditions. Differential games satisfying these conditions are called regular games. The programmed iteration method could be considered a non-smooth version of the dynamic programming method. Initially the programmed iteration method was aimed at studying non-regular differential games. Later it became obvious that the scope of application of programmed iteration method is wider. For example based on results of the programmed iteration method the theory of differential games could be built. One more example is provided in this article. Based on results of programmed iteration method, theorem on convex-concave functions and the theorem on measurable selector of multi-valued map we provide simple proof of well-known regular condition for linear differential game of approach with fixed duration. Bibliogr. 14.

Download

A Necessary And Sufficient Condition For The Existence Of The Value For Positional Differential Game

IFAC Proceedings Volumes, 2009

Simple Compression Code Supporting Random Access and Fast String Matching

Given a sequence S of n symbols over some alphabet Σ, we develop a new compression method that is... more Given a sequence S of n symbols over some alphabet Σ, we develop a new compression method that is (i) very simple to implement; (ii) provides O(1) time random access to any symbol of the original sequence; (iii) allows efficient pattern matching over the compressed sequence. Our simplest solution uses at most 2h + o(h) bits of space, where h = n(H0(S) + 1), and H0(S) is the zeroth-order empirical entropy of S. We discuss a number of improvements and trade-offs over the basic method. The new method is applied to text compression. We also propose average case optimal string matching algorithms.

Download

Simple Random Access Compression

Given a sequence S of n symbols over some alphabet Σ of size σ, we develop new compression method... more Given a sequence S of n symbols over some alphabet Σ of size σ, we develop new compression methods that are (i) very simple to implement; (ii) provide O(1) time random access to any symbol (or short substring) of the original sequence. Our simplest solution uses at most 2h + o(h) bits of space, where h = n(H0(S) + 1), and H0(S) is the zeroth-order empirical entropy of S. We discuss a number of improvements and trade-offs over the basic method. For example, we can achieve n(Hk(S)+1)+o(n(Hk(S)+1)) bits of space, for k = o(log σ(n)). Several applications are discussed, including text compression, (compressed) full-text indexing and string matching.

Download

Simple Compression Code Supporting Random Access and Fast String Matching

Springer eBooks, Jun 26, 2007

Download

Об общей неподвижной точке операторов значения в игре на перехват

A Necessary And Sufficient Condition For The Existence Of The Value For Positional Differential Game

IFAC Proceedings Volumes, 2009

Simple Random Access Compression

Fundamenta Informaticae, 2009

Value operators for the control problem with disturbance

Existence and uniqueness theorem for a generalized Isaacs-Bellman equation

Differential Equations, Jun 1, 2007

Under condition (3), there exists an equilibrium in the small game for an arbitrary choice of the... more

Download

Viscosity solutions and programmed iteration method for Isaacs equation

Efficiency measurement for revenue management

Journal of Revenue and Pricing Management, May 21, 2022

Bloom filters and their applications

Download

Efficiency measurement for revenue management

Journal of Revenue and Pricing Management

Value operators for the control problem with disturbance

2016 International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy's Conference), 2016

On value operators in differential games

Applied Mathematical Sciences, 2015

Download

On Regular Differential Games of Pursuit with Fixed Duration

Download

A Necessary And Sufficient Condition For The Existence Of The Value For Positional Differential Game

IFAC Proceedings Volumes, 2009

Simple Compression Code Supporting Random Access and Fast String Matching

Given a sequence S of n symbols over some alphabet Σ, we develop a new compression method that is... more Given a sequence S of n symbols over some alphabet Σ, we develop a new compression method that is (i) very simple to implement; (ii) provides O(1) time random access to any symbol of the original sequence; (iii) allows efficient pattern matching over the compressed sequence. Our simplest solution uses at most 2h + o(h) bits of space, where h = n(H0(S) + 1), and H0(S) is the zeroth-order empirical entropy of S. We discuss a number of improvements and trade-offs over the basic method. The new method is applied to text compression. We also propose average case optimal string matching algorithms.

Download

Simple Random Access Compression

Download

Fedor Nikitin

Related Authors

Uploads

Papers by Fedor Nikitin

Log In