Matching Items (3)
Filtering by
- All Subjects: covering arrays
- Creators: Richa, Andréa W.
Description
Interference constitutes a major challenge for communication networks operating over a shared medium where availability is imperative. This dissertation studies the problem of designing and analyzing efficient medium access protocols which are robust against strong adversarial jamming. More specifically, four medium access (MAC) protocols (i.e., JADE, ANTIJAM, COMAC, and SINRMAC) which aim to achieve high throughput despite jamming activities under a variety of network and adversary models are presented. We also propose a self-stabilizing leader election protocol, SELECT, that can effectively elect a leader in the network with the existence of a strong adversary. Our protocols can not only deal with internal interference without the exact knowledge on the number of participants in the network, but they are also robust to unintentional or intentional external interference, e.g., due to co-existing networks or jammers. We model the external interference by a powerful adaptive and/or reactive adversary which can jam a (1 − ε)-portion of the time steps, where 0 < ε ≤ 1 is an arbitrary constant. We allow the adversary to be adaptive and to have complete knowledge of the entire protocol history. Moreover, in case the adversary is also reactive, it uses carrier sensing to make informed decisions to disrupt communications. Among the proposed protocols, JADE, ANTIJAM and COMAC are able to achieve Θ(1)-competitive throughput with the presence of the strong adversary; while SINRMAC is the first attempt to apply SINR model (i.e., Signal to Interference plus Noise Ratio), in robust medium access protocols design; the derived principles are also useful to build applications on top of the MAC layer, and we present SELECT, which is an exemplary study for leader election, which is one of the most fundamental tasks in distributed computing.
ContributorsZhang, Jin (Author) / Richa, Andréa W. (Thesis advisor) / Scheideler, Christian (Committee member) / Sen, Arunabha (Committee member) / Xue, Guoliang (Committee member) / Arizona State University (Publisher)
Created2012
Description
Exhaustive testing is generally infeasible except in the smallest of systems. Research
has shown that testing the interactions among fewer (up to 6) components is generally
sufficient while retaining the capability to detect up to 99% of defects. This leads to a
substantial decrease in the number of tests. Covering arrays are combinatorial objects
that guarantee that every interaction is tested at least once.
In the absence of direct constructions, forming small covering arrays is generally
an expensive computational task. Algorithms to generate covering arrays have been
extensively studied yet no single algorithm provides the smallest solution. More
recently research has been directed towards a new technique called post-optimization.
These algorithms take an existing covering array and attempt to reduce its size.
This thesis presents a new idea for post-optimization by representing covering
arrays as graphs. Some properties of these graphs are established and the results are
contrasted with existing post-optimization algorithms. The idea is then generalized to
close variants of covering arrays with surprising results which in some cases reduce
the size by 30%. Applications of the method to generation and test prioritization are
studied and some interesting results are reported.
has shown that testing the interactions among fewer (up to 6) components is generally
sufficient while retaining the capability to detect up to 99% of defects. This leads to a
substantial decrease in the number of tests. Covering arrays are combinatorial objects
that guarantee that every interaction is tested at least once.
In the absence of direct constructions, forming small covering arrays is generally
an expensive computational task. Algorithms to generate covering arrays have been
extensively studied yet no single algorithm provides the smallest solution. More
recently research has been directed towards a new technique called post-optimization.
These algorithms take an existing covering array and attempt to reduce its size.
This thesis presents a new idea for post-optimization by representing covering
arrays as graphs. Some properties of these graphs are established and the results are
contrasted with existing post-optimization algorithms. The idea is then generalized to
close variants of covering arrays with surprising results which in some cases reduce
the size by 30%. Applications of the method to generation and test prioritization are
studied and some interesting results are reported.
ContributorsKaria, Rushang Vinod (Author) / Colbourn, Charles J (Thesis advisor) / Syrotiuk, Violet (Committee member) / Richa, Andréa W. (Committee member) / Arizona State University (Publisher)
Created2015
Description
Modern software and hardware systems are composed of a large number of components. Often different components of a system interact with each other in unforeseen and undesired ways to cause failures. Covering arrays are a useful mathematical tool for testing all possible t-way interactions among the components of a system.
The two major issues concerning covering arrays are explicit construction of a covering array, and exact or approximate determination of the covering array number---the minimum size of a covering array. Although these problems have been investigated extensively for the last couple of decades, in this thesis we present significant improvements on both of these questions using tools from the probabilistic method and randomized algorithms.
First, a series of improvements is developed on the previously known upper bounds on covering array numbers. An estimate for the discrete Stein-Lovász-Johnson bound is derived and the Stein- Lovász -Johnson bound is improved upon using an alteration strategy. Then group actions on the set of symbols are explored to establish two asymptotic upper bounds on covering array numbers that are tighter than any of the presently known bounds.
Second, an algorithmic paradigm, called the two-stage framework, is introduced for covering array construction. A number of concrete algorithms from this framework are analyzed, and it is shown that they outperform current methods in the range of parameter values that are of practical relevance. In some cases, a reduction in the number of tests by more than 50% is achieved.
Third, the Lovász local lemma is applied on covering perfect hash families to obtain an upper bound on covering array numbers that is tightest of all known bounds. This bound leads to a Moser-Tardos type algorithm that employs linear algebraic computation over finite fields to construct covering arrays. In some cases, this algorithm outperforms currently used methods by more than an 80% margin.
Finally, partial covering arrays are introduced to investigate a few practically relevant relaxations of the covering requirement. Using probabilistic methods, bounds are obtained on partial covering arrays that are significantly smaller than for covering arrays. Also, randomized algorithms are provided that construct such arrays in expected polynomial time.
The two major issues concerning covering arrays are explicit construction of a covering array, and exact or approximate determination of the covering array number---the minimum size of a covering array. Although these problems have been investigated extensively for the last couple of decades, in this thesis we present significant improvements on both of these questions using tools from the probabilistic method and randomized algorithms.
First, a series of improvements is developed on the previously known upper bounds on covering array numbers. An estimate for the discrete Stein-Lovász-Johnson bound is derived and the Stein- Lovász -Johnson bound is improved upon using an alteration strategy. Then group actions on the set of symbols are explored to establish two asymptotic upper bounds on covering array numbers that are tighter than any of the presently known bounds.
Second, an algorithmic paradigm, called the two-stage framework, is introduced for covering array construction. A number of concrete algorithms from this framework are analyzed, and it is shown that they outperform current methods in the range of parameter values that are of practical relevance. In some cases, a reduction in the number of tests by more than 50% is achieved.
Third, the Lovász local lemma is applied on covering perfect hash families to obtain an upper bound on covering array numbers that is tightest of all known bounds. This bound leads to a Moser-Tardos type algorithm that employs linear algebraic computation over finite fields to construct covering arrays. In some cases, this algorithm outperforms currently used methods by more than an 80% margin.
Finally, partial covering arrays are introduced to investigate a few practically relevant relaxations of the covering requirement. Using probabilistic methods, bounds are obtained on partial covering arrays that are significantly smaller than for covering arrays. Also, randomized algorithms are provided that construct such arrays in expected polynomial time.
ContributorsSarakāra, Kauśika (Author) / Colbourn, Charles J. (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Richa, Andréa W. (Committee member) / Syrotiuk, Violet R. (Committee member) / Arizona State University (Publisher)
Created2016