Search results for "Telecommunication"

A note on the support of block idempotents

1994

Computing the Probability for Data Loss in Two-Dimensional Parity RAIDs

2017

Parity RAIDs are used to protect storage systems against disk failures. The idea is to add redundancy to the system by storing the parity of subsets of disks on extra parity disks. A simple two-dimensional scheme is the one in which the data disks are arranged in a rectangular grid, and every row and column is extended by one disk which stores the parity of it.In this paper we describe several two-dimensional parity RAIDs and analyse, for each of them, the probability for dataloss given that f random disks fail. This probability can be used to determine the overall probability using the model of Hafner and Rao. We reduce subsets of the forest counting problem to the different cases and show…

Enumeration of Łukasiewicz paths modulo some patterns

2019

Abstract For any pattern α of length at most two, we enumerate equivalence classes of Łukasiewicz paths of length n ≥ 0 where two paths are equivalent whenever the occurrence positions of α are identical on these paths. As a byproduct, we give a constructive bijection between Motzkin paths and some equivalence classes of Łukasiewicz paths.

A Tight Lower Bound on Certificate Complexity in Terms of Block Sensitivity and Sensitivity

2014

Sensitivity, certificate complexity and block sensitivity are widely used Boolean function complexity measures. A longstanding open problem, proposed by Nisan and Szegedy [7], is whether sensitivity and block sensitivity are polynomially related. Motivated by the constructions of functions which achieve the largest known separations, we study the relation between 1-certificate complexity and 0-sensitivity and 0-block sensitivity.

A Generalization of Girod’s Bidirectional Decoding Method to Codes with a Finite Deciphering Delay

2012

In this paper we generalize an encoding method due to Girod (cf. [6]) using prefix codes, that allows a bidirectional decoding of the encoded messages. In particular we generalize it to any finite alphabet A, to any operation defined on A, to any code with finite deciphering delay and to any key x ∈ A+ , on a length depending on the deciphering delay. We moreover define, as in [4], a deterministic transducer for such generalized method. We prove that, fixed a code X ∈ A* with finite deciphering delay and a key x ∈ A *, the transducers associated to different operations are isomorphic as unlabelled graphs. We also prove that, for a fixed code X with finite deciphering delay, transducers asso…

Randomized renaming in shared memory systems.

2021

Abstract Renaming is a task in distributed computing where n processes are assigned new names from a name space of size m . The problem is called tight if m = n , and loose if m > n . In recent years renaming came to the fore again and new algorithms were developed. For tight renaming in asynchronous shared memory systems, Alistarh et al. describe a construction based on the AKS network that assigns all names within O ( log n ) steps per process. They also show that, depending on the size of the name space, loose renaming can be done considerably faster. For m = ( 1 + ϵ ) ⋅ n and constant ϵ , they achieve a step complexity of O ( log log n ) . In this paper we consider tight as well as loos…

Minimum node weight spanning trees searching algorithm for broadcast transmission in sensor networks

2017

A minimum node weight spanning tree in a weighted, directed graph is a tree whose node with maximum out-weight is minimal among all spanning trees. This type of trees are important because they appear in the solutions of the maximum lifetime broadcasting problem in wireless sensor networks. In a complete graph build of N nodes there are NN-2 spanning trees and to find such trees it is necessary to perform more than O(NN-2) operations. In this paper we propose an algorithm for searching the minimum node weight spanning trees in the graph. In the proposed algorithm, instead of calculating the symbolic determinant of the generalized Laplacian matrix, numerical operations on its exponents are p…

Uncountable Realtime Probabilistic Classes

2018

We investigate the minimal cases for realtime probabilistic machines that can define uncountably many languages with bounded error. We show that logarithmic space is enough for realtime PTMs on unary languages. On non-unary case, we obtain the same result for double logarithmic space, which is also tight. When replacing the work tape with a few counters, we can still achieve similar results for unary linear-space two-counter automata, unary sublinear-space three-counter automata, and non-unary sublinear-space two-counter automata. We also show how to slightly improve the sublinear-space constructions by using more counters.

The Spanning Tree based Approach for Solving the Shortest Path Problem in Social Graphs

2016

Nowadays there are many social media sites with a very large number of users. Users of social media sites and relationships between them can be modelled as a graph. Such graphs can be analysed using methods from social network analysis (SNA). Many measures used in SNA rely on computation of shortest paths between nodes of a graph. There are many shortest path algorithms, but the majority of them suits only for small graphs, or work only with road network graphs that are fundamentally different from social graphs. This paper describes an efficient shortest path searching algorithm suitable for large social graphs. The described algorithm extends the Atlas algorithm. The proposed algorithm so…

Digital signal processing for rail monitoring by means of ultrasonic guided waves

2007

Recent train accidents have reaffirmed the need for developing rail defect detection systems that are more effective than those used today. One of the recent developments in rail inspection is the use of ultrasonic guided waves (UGWs) and non-contact probing techniques to target transverse-type defects. Besides the obvious advantages of non-contact probing, that include robustness and a potential for large inspection speed, such a system can theoretically detect transverse defects under horizontal shelling or head checks. This paper demonstrates the effectiveness of digital signal processing to enhance the damage detection sensitivity of the non-contact system. The method proposed here comb…