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- All Subjects: Computer Science
- Genre: Doctoral Dissertation
- Status: Published
Description
Communication networks, both wired and wireless, are expected to have a certain level of fault-tolerance capability.These networks are also expected to ensure a graceful degradation in performance when some of the network components fail. Traditional studies on fault tolerance in communication networks, for the most part, make no assumptions regarding the location of node/link faults, i.e., the faulty nodes and links may be close to each other or far from each other. However, in many real life scenarios, there exists a strong spatial correlation among the faulty nodes and links. Such failures are often encountered in disaster situations, e.g., natural calamities or enemy attacks. In presence of such region-based faults, many of traditional network analysis and fault-tolerant metrics, that are valid under non-spatially correlated faults, are no longer applicable. To this effect, the main thrust of this research is design and analysis of robust networks in presence of such region-based faults. One important finding of this research is that if some prior knowledge is available on the maximum size of the region that might be affected due to a region-based fault, this piece of knowledge can be effectively utilized for resource efficient design of networks. It has been shown in this dissertation that in some scenarios, effective utilization of this knowledge may result in substantial saving is transmission power in wireless networks. In this dissertation, the impact of region-based faults on the connectivity of wireless networks has been studied and a new metric, region-based connectivity, is proposed to measure the fault-tolerance capability of a network. In addition, novel metrics, such as the region-based component decomposition number(RBCDN) and region-based largest component size(RBLCS) have been proposed to capture the network state, when a region-based fault disconnects the network. Finally, this dissertation presents efficient resource allocation techniques that ensure tolerance against region-based faults, in distributed file storage networks and data center networks.
ContributorsBanerjee, Sujogya (Author) / Sen, Arunabha (Thesis advisor) / Xue, Guoliang (Committee member) / Richa, Andrea (Committee member) / Hurlbert, Glenn (Committee member) / Arizona State University (Publisher)
Created2013
Description
As networks are playing an increasingly prominent role in different aspects of our lives, there is a growing awareness that improving their performance is of significant importance. In order to enhance performance of networks, it is essential that scarce networking resources be allocated smartly to match the continuously changing network environment. This dissertation focuses on two different kinds of networks - communication and social, and studies resource allocation problems in these networks. The study on communication networks is further divided into different networking technologies - wired and wireless, optical and mobile, airborne and terrestrial. Since nodes in an airborne network (AN) are heterogeneous and mobile, the design of a reliable and robust AN is highly complex. The dissertation studies connectivity and fault-tolerance issues in ANs and proposes algorithms to compute the critical transmission range in fault free, faulty and delay tolerant scenarios. Just as in the case of ANs, power optimization and fault tolerance are important issues in wireless sensor networks (WSN). In a WSN, a tree structure is often used to deliver sensor data to a sink node. In a tree, failure of a node may disconnect the tree. The dissertation investigates the problem of enhancing the fault tolerance capability of data gathering trees in WSN. The advent of OFDM technology provides an opportunity for efficient resource utilization in optical networks and also introduces a set of novel problems, such as routing and spectrum allocation (RSA) problem. This dissertation proves that RSA problem is NP-complete even when the network topology is a chain, and proposes approximation algorithms. In the domain of social networks, the focus of this dissertation is study of influence propagation in presence of active adversaries. In a social network multiple vendors may attempt to influence the nodes in a competitive fashion. This dissertation investigates the scenario where the first vendor has already chosen a set of nodes and the second vendor, with the knowledge of the choice of the first, attempts to identify a smallest set of nodes so that after the influence propagation, the second vendor's market share is larger than the first.
ContributorsShirazipourazad, Shahrzad (Author) / Sen, Arunabha (Committee member) / Xue, Guoliang (Committee member) / Richa, Andrea (Committee member) / Saripalli, Srikanth (Committee member) / Arizona State University (Publisher)
Created2014
Description
Resource allocation is one of the most challenging issues policy decision makers must address. The objective of this thesis is to explore the resource allocation from an economical perspective, i.e., how to purchase resources in order to satisfy customers' requests. In this thesis, we attend to answer the question: when and how to buy resources to fulfill customers' demands with minimum costs?
The first topic studied in this thesis is resource allocation in cloud networks. Cloud computing heralded an era where resources (such as computation and storage) can be scaled up and down elastically and on demand. This flexibility is attractive for its cost effectiveness: the cloud resource price depends on the actual utilization over time. This thesis studies two critical problems in cloud networks, focusing on the economical aspects of the resource allocation in the cloud/virtual networks, and proposes six algorithms to address the resource allocation problems for different discount models. The first problem attends a scenario where the virtual network provider offers different contracts to the service provider. Four algorithms for resource contract migration are proposed under two pricing models: Pay-as-You-Come and Pay-as-You-Go. The second problem explores a scenario where a cloud provider offers k contracts each with a duration and a rate respectively and a customer buys these contracts in order to satisfy its resource demand. This work shows that this problem can be seen as a 2-dimensional generalization of the classic online parking permit problem, and present a k-competitive online algorithm and an optimal online algorithm.
The second topic studied in this thesis is to explore how resource allocation and purchasing strategies work in our daily life. For example, is it worth buying a Yoga pass which costs USD 100 for ten entries, although it will expire at the end of this year? Decisions like these are part of our daily life, yet, not much is known today about good online strategies to buy discount vouchers with expiration dates. This work hence introduces a Discount Voucher Purchase Problem (DVPP). It aims to optimize the strategies for buying discount vouchers, i.e., coupons, vouchers, groupons which are valid only during a certain time period. The DVPP comes in three flavors: (1) Once Expire Lose Everything (OELE): Vouchers lose their entire value after expiration. (2) Once Expire Lose Discount (OELD): Vouchers lose their discount value after expiration. (3) Limited Purchasing Window (LPW): Vouchers have the property of OELE and can only be bought during a certain time window.
This work explores online algorithms with a provable competitive ratio against a clairvoyant offline algorithm, even in the worst case. In particular, this work makes the following contributions: we present a 4-competitive algorithm for OELE, an 8-competitive algorithm for OELD, and a lower bound for LPW. We also present an optimal offline algorithm for OELE and LPW, and show it is a 2-approximation solution for OELD.
The first topic studied in this thesis is resource allocation in cloud networks. Cloud computing heralded an era where resources (such as computation and storage) can be scaled up and down elastically and on demand. This flexibility is attractive for its cost effectiveness: the cloud resource price depends on the actual utilization over time. This thesis studies two critical problems in cloud networks, focusing on the economical aspects of the resource allocation in the cloud/virtual networks, and proposes six algorithms to address the resource allocation problems for different discount models. The first problem attends a scenario where the virtual network provider offers different contracts to the service provider. Four algorithms for resource contract migration are proposed under two pricing models: Pay-as-You-Come and Pay-as-You-Go. The second problem explores a scenario where a cloud provider offers k contracts each with a duration and a rate respectively and a customer buys these contracts in order to satisfy its resource demand. This work shows that this problem can be seen as a 2-dimensional generalization of the classic online parking permit problem, and present a k-competitive online algorithm and an optimal online algorithm.
The second topic studied in this thesis is to explore how resource allocation and purchasing strategies work in our daily life. For example, is it worth buying a Yoga pass which costs USD 100 for ten entries, although it will expire at the end of this year? Decisions like these are part of our daily life, yet, not much is known today about good online strategies to buy discount vouchers with expiration dates. This work hence introduces a Discount Voucher Purchase Problem (DVPP). It aims to optimize the strategies for buying discount vouchers, i.e., coupons, vouchers, groupons which are valid only during a certain time period. The DVPP comes in three flavors: (1) Once Expire Lose Everything (OELE): Vouchers lose their entire value after expiration. (2) Once Expire Lose Discount (OELD): Vouchers lose their discount value after expiration. (3) Limited Purchasing Window (LPW): Vouchers have the property of OELE and can only be bought during a certain time window.
This work explores online algorithms with a provable competitive ratio against a clairvoyant offline algorithm, even in the worst case. In particular, this work makes the following contributions: we present a 4-competitive algorithm for OELE, an 8-competitive algorithm for OELD, and a lower bound for LPW. We also present an optimal offline algorithm for OELE and LPW, and show it is a 2-approximation solution for OELD.
ContributorsHu, Xinhui (Author) / Richa, Andrea (Thesis advisor) / Schmid, Stefan (Committee member) / Sen, Arunabha (Committee member) / Xue, Guoliang (Committee member) / Arizona State University (Publisher)
Created2015
Description
This dissertation studies routing in small-world networks such as grids plus long-range edges and real networks. Kleinberg showed that geography-based greedy routing in a grid-based network takes an expected number of steps polylogarithmic in the network size, thus justifying empirical efficiency observed beginning with Milgram. A counterpart for the grid-based model is provided; it creates all edges deterministically and shows an asymptotically matching upper bound on the route length. The main goal is to improve greedy routing through a decentralized machine learning process. Two considered methods are based on weighted majority and an algorithm of de Farias and Megiddo, both learning from feedback using ensembles of experts. Tests are run on both artificial and real networks, with decentralized spectral graph embedding supplying geometric information for real networks where it is not intrinsically available. An important measure analyzed in this work is overpayment, the difference between the cost of the method and that of the shortest path. Adaptive routing overtakes greedy after about a hundred or fewer searches per node, consistently across different network sizes and types. Learning stabilizes, typically at overpayment of a third to a half of that by greedy. The problem is made more difficult by eliminating the knowledge of neighbors' locations or by introducing uncooperative nodes. Even under these conditions, the learned routes are usually better than the greedy routes. The second part of the dissertation is related to the community structure of unannotated networks. A modularity-based algorithm of Newman is extended to work with overlapping communities (including considerably overlapping communities), where each node locally makes decisions to which potential communities it belongs. To measure quality of a cover of overlapping communities, a notion of a node contribution to modularity is introduced, and subsequently the notion of modularity is extended from partitions to covers. The final part considers a problem of network anonymization, mostly by the means of edge deletion. The point of interest is utility preservation. It is shown that a concentration on the preservation of routing abilities might damage the preservation of community structure, and vice versa.
ContributorsBakun, Oleg (Author) / Konjevod, Goran (Thesis advisor) / Richa, Andrea (Thesis advisor) / Syrotiuk, Violet R. (Committee member) / Czygrinow, Andrzej (Committee member) / Arizona State University (Publisher)
Created2011
Description
In the realm of network science, many topics can be abstracted as graph problems, such as routing, connectivity enhancement, resource/frequency allocation and so on. Though most of them are NP-hard to solve, heuristics as well as approximation algorithms are proposed to achieve reasonably good results. Accordingly, this dissertation studies graph related problems encountered in real applications. Two problems studied in this dissertation are derived from wireless network, two more problems studied are under scenarios of FIWI and optical network, one more problem is in Radio- Frequency Identification (RFID) domain and the last problem is inspired by satellite deployment.
The objective of most of relay nodes placement problems, is to place the fewest number of relay nodes in the deployment area so that the network, formed by the sensors and the relay nodes, is connected. Under the fixed budget scenario, the expense involved in procuring the minimum number of relay nodes to make the network connected, may exceed the budget. In this dissertation, we study a family of problems whose goal is to design a network with “maximal connectedness” or “minimal disconnectedness”, subject to a fixed budget constraint. Apart from “connectivity”, we also study relay node problem in which degree constraint is considered. The balance of reducing the degree of the network while maximizing communication forms the basis of our d-degree minimum arrangement(d-MA) problem. In this dissertation, we look at several approaches to solving the generalized d-MA problem where we embed a graph onto a subgraph of a given degree.
In recent years, considerable research has been conducted on optical and FIWI networks. Utilizing a recently proposed concept “candidate trees” in optical network, this dissertation studies counting problem on complete graphs. Closed form expressions are given for certain cases and a polynomial counting algorithm for general cases is also presented. Routing plays a major role in FiWi networks. Accordingly to a novel path length metric which emphasizes on “heaviest edge”, this dissertation proposes a polynomial algorithm on single path computation. NP-completeness proof as well as approximation algorithm are presented for multi-path routing.
Radio-frequency identification (RFID) technology is extensively used at present for identification and tracking of a multitude of objects. In many configurations, simultaneous activation of two readers may cause a “reader collision” when tags are present in the intersection of the sensing ranges of both readers. This dissertation ad- dresses slotted time access for Readers and tries to provide a collision-free scheduling scheme while minimizing total reading time.
Finally, this dissertation studies a monitoring problem on the surface of the earth for significant environmental, social/political and extreme events using satellites as sensors. It is assumed that the impact of a significant event spills into neighboring regions and there will be corresponding indicators. Careful deployment of sensors, utilizing “Identifying Codes”, can ensure that even though the number of deployed sensors is fewer than the number of regions, it may be possible to uniquely identify the region where the event has taken place.
The objective of most of relay nodes placement problems, is to place the fewest number of relay nodes in the deployment area so that the network, formed by the sensors and the relay nodes, is connected. Under the fixed budget scenario, the expense involved in procuring the minimum number of relay nodes to make the network connected, may exceed the budget. In this dissertation, we study a family of problems whose goal is to design a network with “maximal connectedness” or “minimal disconnectedness”, subject to a fixed budget constraint. Apart from “connectivity”, we also study relay node problem in which degree constraint is considered. The balance of reducing the degree of the network while maximizing communication forms the basis of our d-degree minimum arrangement(d-MA) problem. In this dissertation, we look at several approaches to solving the generalized d-MA problem where we embed a graph onto a subgraph of a given degree.
In recent years, considerable research has been conducted on optical and FIWI networks. Utilizing a recently proposed concept “candidate trees” in optical network, this dissertation studies counting problem on complete graphs. Closed form expressions are given for certain cases and a polynomial counting algorithm for general cases is also presented. Routing plays a major role in FiWi networks. Accordingly to a novel path length metric which emphasizes on “heaviest edge”, this dissertation proposes a polynomial algorithm on single path computation. NP-completeness proof as well as approximation algorithm are presented for multi-path routing.
Radio-frequency identification (RFID) technology is extensively used at present for identification and tracking of a multitude of objects. In many configurations, simultaneous activation of two readers may cause a “reader collision” when tags are present in the intersection of the sensing ranges of both readers. This dissertation ad- dresses slotted time access for Readers and tries to provide a collision-free scheduling scheme while minimizing total reading time.
Finally, this dissertation studies a monitoring problem on the surface of the earth for significant environmental, social/political and extreme events using satellites as sensors. It is assumed that the impact of a significant event spills into neighboring regions and there will be corresponding indicators. Careful deployment of sensors, utilizing “Identifying Codes”, can ensure that even though the number of deployed sensors is fewer than the number of regions, it may be possible to uniquely identify the region where the event has taken place.
ContributorsZhou, Chenyang (Author) / Richa, Andrea (Thesis advisor) / Sen, Arunabha (Thesis advisor) / Xue, Guoliang (Committee member) / Walkowiak, Krzysztof (Committee member) / Arizona State University (Publisher)
Created2019
Description
We live in a networked world with a multitude of networks, such as communication networks, electric power grid, transportation networks and water distribution networks, all around us. In addition to such physical (infrastructure) networks, recent years have seen tremendous proliferation of social networks, such as Facebook, Twitter, LinkedIn, Instagram, Google+ and others. These powerful social networks are not only used for harnessing revenue from the infrastructure networks, but are also increasingly being used as “non-conventional sensors” for monitoring the infrastructure networks. Accordingly, nowadays, analyses of social and infrastructure networks go hand-in-hand. This dissertation studies resource allocation problems encountered in this set of diverse, heterogeneous, and interdependent networks. Three problems studied in this dissertation are encountered in the physical network domain while the three other problems studied are encountered in the social network domain.
The first problem from the infrastructure network domain relates to distributed files storage scheme with a goal of enhancing robustness of data storage by making it tolerant against large scale geographically-correlated failures. The second problem relates to placement of relay nodes in a deployment area with multiple sensor nodes with a goal of augmenting connectivity of the resulting network, while staying within the budget specifying the maximum number of relay nodes that can be deployed. The third problem studied in this dissertation relates to complex interdependencies that exist between infrastructure networks, such as power grid and communication network. The progressive recovery problem in an interdependent network is studied whose goal is to maximize system utility over the time when recovery process of failed entities takes place in a sequential manner.
The three problems studied from the social network domain relate to influence propagation in adversarial environment and political sentiment assessment in various states in a country with a goal of creation of a “political heat map” of the country. In the first problem of the influence propagation domain, the goal of the second player is to restrict the influence of the first player, while in the second problem the goal of the second player is to have a larger market share with least amount of initial investment.
The first problem from the infrastructure network domain relates to distributed files storage scheme with a goal of enhancing robustness of data storage by making it tolerant against large scale geographically-correlated failures. The second problem relates to placement of relay nodes in a deployment area with multiple sensor nodes with a goal of augmenting connectivity of the resulting network, while staying within the budget specifying the maximum number of relay nodes that can be deployed. The third problem studied in this dissertation relates to complex interdependencies that exist between infrastructure networks, such as power grid and communication network. The progressive recovery problem in an interdependent network is studied whose goal is to maximize system utility over the time when recovery process of failed entities takes place in a sequential manner.
The three problems studied from the social network domain relate to influence propagation in adversarial environment and political sentiment assessment in various states in a country with a goal of creation of a “political heat map” of the country. In the first problem of the influence propagation domain, the goal of the second player is to restrict the influence of the first player, while in the second problem the goal of the second player is to have a larger market share with least amount of initial investment.
ContributorsMazumder, Anisha (Author) / Sen, Arunabha (Thesis advisor) / Richa, Andrea (Committee member) / Xue, Guoliang (Committee member) / Reisslein, Martin (Committee member) / Arizona State University (Publisher)
Created2016
Description
Imagine that we have a piece of matter that can change its physical properties like its shape, density, conductivity, or color in a programmable fashion based on either user input or autonomous sensing. This is the vision behind what is commonly known as programmable matter. Envisioning systems of nano-sensors devices, programmable matter consists of systems of simple computational elements, called particles, that can establish and release bonds, compute, and can actively move in a self-organized way. In this dissertation the feasibility of solving fundamental problems relevant for programmable matter is investigated. As a model for such self-organizing particle systems (SOPS), the geometric amoebot model is introduced. In this model, particles only have local information and have modest computational power. They achieve locomotion by expanding and contracting, which resembles the behavior of amoeba. Under this model, efficient local-control algorithms for the leader election problem in SOPS are presented. As a central problem for programmable matter, shape formation problems are then studied. The limitations of solving the leader election problem and the shape formation problem on a more general version of the amoebot model are also discussed. The \smart paint" problem is also studied which aims at having the particles self-organize in order to uniformly coat the surface of an object of arbitrary shape and size, forming multiple coating layers if necessary. A Universal Coating algorithm is presented and shown to be asymptotically worst-case optimal both in terms of time with high probability and work. In particular, the algorithm always terminates within a linear number of rounds with high probability. A linear lower bound on the competitive gap between fully local coating algorithms and coating algorithms that rely on global information is presented, which implies that the proposed algorithm is also optimal in a competitive sense. Simulation results show that the competitive ratio of the proposed algorithm may be better than linear in practice. Developed algorithms utilize only local control, require only constant-size memory particles, and are asymptotically optimal in terms of the total number of particle movements needed to reach the desired shape configuration.
ContributorsDerakhshandeh, Zahra (Author) / Richa, Andrea (Thesis advisor) / Sen, Arunabha (Thesis advisor) / Xue, Guoliang (Committee member) / Scheideler, Christian (Committee member) / Arizona State University (Publisher)
Created2017
Description
While network problems have been addressed using a central administrative domain with a single objective, the devices in most networks are actually not owned by a single entity but by many individual entities. These entities make their decisions independently and selfishly, and maybe cooperate with a small group of other entities only when this form of coalition yields a better return. The interaction among multiple independent decision-makers necessitates the use of game theory, including economic notions related to markets and incentives. In this dissertation, we are interested in modeling, analyzing, addressing network problems caused by the selfish behavior of network entities. First, we study how the selfish behavior of network entities affects the system performance while users are competing for limited resource. For this resource allocation domain, we aim to study the selfish routing problem in networks with fair queuing on links, the relay assignment problem in cooperative networks, and the channel allocation problem in wireless networks. Another important aspect of this dissertation is the study of designing efficient mechanisms to incentivize network entities to achieve certain system objective. For this incentive mechanism domain, we aim to motivate wireless devices to serve as relays for cooperative communication, and to recruit smartphones for crowdsourcing. In addition, we apply different game theoretic approaches to problems in security and privacy domain. For this domain, we aim to analyze how a user could defend against a smart jammer, who can quickly learn about the user's transmission power. We also design mechanisms to encourage mobile phone users to participate in location privacy protection, in order to achieve k-anonymity.
ContributorsYang, Dejun (Author) / Xue, Guoliang (Thesis advisor) / Richa, Andrea (Committee member) / Sen, Arunabha (Committee member) / Zhang, Junshan (Committee member) / Arizona State University (Publisher)
Created2013
Description
A storage system requiring file redundancy and on-line repairability can be represented as a Steiner system, a combinatorial design with the property that every $t$-subset of its points occurs in exactly one of its blocks. Under this representation, files are the points and storage units are the blocks of the Steiner system, or vice-versa. Often, the popularities of the files of such storage systems run the gamut, with some files receiving hardly any attention, and others receiving most of it. For such systems, minimizing the difference in the collective popularity between any two storage units is nontrivial; this is the access balancing problem. With regard to the representative Steiner system, the access balancing problem in its simplest form amounts to constructing either a point or block labelling: an assignment of a set of integer labels (popularity ranks) to the Steiner system's point set or block set, respectively, requiring of the former assignment that the sums of the labelled points of any two blocks differ as little as possible and of the latter that the sums of the labels assigned to the containing blocks of any two distinct points differ as little as possible. The central aim of this dissertation is to supply point and block labellings for Steiner systems of block size greater than three, for which up to this point no attempt has been made. Four major results are given in this connection. First, motivated by the close connection between the size of the independent sets of a Steiner system and the quality of its labellings, a Steiner triple system of any admissible order is constructed with a pair of disjoint independent sets of maximum cardinality. Second, the spectrum of resolvable Bose triple systems is determined in order to label some Steiner 2-designs with block size four. Third, several kinds of independent sets are used to point-label Steiner 2-designs with block size four. Finally, optimal and close to optimal block labellings are given for an infinite class of 1-rotational resolvable Steiner 2-designs with arbitrarily large block size by exploiting their underlying group-theoretic properties.
ContributorsLusi, Dylan (Author) / Colbourn, Charles J (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Fainekos, Georgios (Committee member) / Richa, Andrea (Committee member) / Arizona State University (Publisher)
Created2021
Description
The construction of many families of combinatorial objects remains a challenging problem. A t-restriction is an array where a predicate is satisfied for every t columns; an example is a perfect hash family (PHF). The composition of a PHF and any t-restriction satisfying predicate P yields another t-restriction also satisfying P with more columns than the original t-restriction had. This thesis concerns three approaches in determining the smallest size of PHFs.
Firstly, hash families in which the associated property is satisfied at least some number lambda times are considered, called higher-index, which guarantees redundancy when constructing t-restrictions. Some direct and optimal constructions of hash families of higher index are given. A new recursive construction is established that generalizes previous results and generates higher-index PHFs with more columns. Probabilistic methods are employed to obtain an upper bound on the optimal size of higher-index PHFs when the number of columns is large. A new deterministic algorithm is developed that generates such PHFs meeting this bound, and computational results are reported.
Secondly, a restriction on the structure of PHFs is introduced, called fractal, a method from Blackburn. His method is extended in several ways; from homogeneous hash families (every row has the same number of symbols) to heterogeneous ones; and to distributing hash families, a relaxation of the predicate for PHFs. Recursive constructions with fractal hash families as ingredients are given, and improve upon on the best-known sizes of many PHFs.
Thirdly, a method of Colbourn and Lanus is extended in which they horizontally copied a given hash family and greedily applied transformations to each copy. Transformations of existential t-restrictions are introduced, which allow for the method to be applicable to any t-restriction having structure like those of hash families. A genetic algorithm is employed for finding the "best" such transformations. Computational results of the GA are reported using PHFs, as the number of transformations permitted is large compared to the number of symbols. Finally, an analysis is given of what trade-offs exist between computation time and the number of t-sets left not satisfying the predicate.
Firstly, hash families in which the associated property is satisfied at least some number lambda times are considered, called higher-index, which guarantees redundancy when constructing t-restrictions. Some direct and optimal constructions of hash families of higher index are given. A new recursive construction is established that generalizes previous results and generates higher-index PHFs with more columns. Probabilistic methods are employed to obtain an upper bound on the optimal size of higher-index PHFs when the number of columns is large. A new deterministic algorithm is developed that generates such PHFs meeting this bound, and computational results are reported.
Secondly, a restriction on the structure of PHFs is introduced, called fractal, a method from Blackburn. His method is extended in several ways; from homogeneous hash families (every row has the same number of symbols) to heterogeneous ones; and to distributing hash families, a relaxation of the predicate for PHFs. Recursive constructions with fractal hash families as ingredients are given, and improve upon on the best-known sizes of many PHFs.
Thirdly, a method of Colbourn and Lanus is extended in which they horizontally copied a given hash family and greedily applied transformations to each copy. Transformations of existential t-restrictions are introduced, which allow for the method to be applicable to any t-restriction having structure like those of hash families. A genetic algorithm is employed for finding the "best" such transformations. Computational results of the GA are reported using PHFs, as the number of transformations permitted is large compared to the number of symbols. Finally, an analysis is given of what trade-offs exist between computation time and the number of t-sets left not satisfying the predicate.
ContributorsDougherty, Ryan Edward (Author) / Colbourn, Charles J (Thesis advisor) / Czygrinow, Andrzej (Committee member) / Forrest, Stephanie (Committee member) / Richa, Andrea (Committee member) / Arizona State University (Publisher)
Created2019