title: Star Decompositions of Bipartite Graphs

authors: Lim, Nick Jin Sean

subjects: Graph Decomposition

abstract: In Chapter 1, we will introduce the definitions and the notations used throughout this thesis. We will also survey some prior research pertaining to graph decompositions, with special emphasis on star-decompositions and decompositions of bipartite graphs. Here we will also introduce some basic algorithms and lemmas that are used in this thesis.

In Chapter 2, we will focus primarily on decomposition of complete bipartite graphs. We will also cover the necessary and sufficient conditions for the decomposition of complete bipartite graphs minus a 1-factor, also known as crown graphs and show that all complete bipartite graphs and crown graphs have  a decomposition into stars when certain necessary conditions for the decomposition are met. This is an extension of the results given in "On claw-decomposition of complete graphs and complete bigraphs" by Yamamoto, et. al. We will propose a construction for the decomposition of the graphs. 

In Chapter 3, we focus on the decomposition of complete equipartite tripartite graphs. This result is similar to the results of "On Claw-decomposition of complete multipartite graphs" by Ushio and Yamamoto. Our proof is again by construction and we propose how it might extend to equipartite multipartite graphs. We will also discuss the 3-star decomposition of complete tripartite graphs.

In Chapter 4 , we will discuss the star decomposition of 4-regular bipartite graphs, with particular emphasis on the decomposition of 4-regular bipartite graphs into 3-stars. We will propose methods to extend our strategies to model the problem as an optimization problem. We will also look into the probabilistic method discussed in "Tree decomposition of Graphs" by Yuster and how we might modify the results of this paper to star decompositions of bipartite graphs. 

In Chapter 5, we summarize the findings in this thesis, and discuss the future work and research in star decompositions of bipartite and multipartite graphs.

text: Star Decompositions of Bipartite Graphs In Chapter 1, we will introduce the definitions and the notations used throughout this thesis. We will also survey some prior research pertaining to graph decompositions, with special emphasis on star-decompositions and decompositions of bipartite graphs. Here we will also introduce some basic algorithms and lemmas that are used in this thesis.

In Chapter 2, we will focus primarily on decomposition of complete bipartite graphs. We will also cover the necessary and sufficient conditions for the decomposition of complete bipartite graphs minus a 1-factor, also known as crown graphs and show that all complete bipartite graphs and crown graphs have  a decomposition into stars when certain necessary conditions for the decomposition are met. This is an extension of the results given in "On claw-decomposition of complete graphs and complete bigraphs" by Yamamoto, et. al. We will propose a construction for the decomposition of the graphs. 

In Chapter 3, we focus on the decomposition of complete equipartite tripartite graphs. This result is similar to the results of "On Claw-decomposition of complete multipartite graphs" by Ushio and Yamamoto. Our proof is again by construction and we propose how it might extend to equipartite multipartite graphs. We will also discuss the 3-star decomposition of complete tripartite graphs.

In Chapter 4 , we will discuss the star decomposition of 4-regular bipartite graphs, with particular emphasis on the decomposition of 4-regular bipartite graphs into 3-stars. We will propose methods to extend our strategies to model the problem as an optimization problem. We will also look into the probabilistic method discussed in "Tree decomposition of Graphs" by Yuster and how we might modify the results of this paper to star decompositions of bipartite graphs. 

In Chapter 5, we summarize the findings in this thesis, and discuss the future work and research in star decompositions of bipartite and multipartite graphs.

year: 2015

title: Good vibrations: artificial ambience-based relay attack detection

authors: Gurulian, Iakovos

subjects: computer science

abstract: Relay attacks are passive man in the middle attacks, aiming to extend the physical distance of devices involved in a transaction beyond their operating environment, within the restricted time-frame. In the field of smartphones, proposals have been put forward suggesting sensing the natural ambient environment as an effective Proximity and Relay Attack Detection (PRAD) mechanism. However, these proposals are not in compliance with industry imposed constraints (e.g. EMV and ITSO) mandating that transactions should complete within a certain time-frame (e.g. 500ms for EMV contactless transactions). The generation of an artificial ambient environment (AAE) using peripherals of the transaction devices has shown positive results when using infrared light as an AAE actuator. In this paper we propose the use of vibration as an alternative AAE actuator. We empirically evaluated the effectiveness of the proposed solution as a PRAD mechanism on an experimental test-bed that we deployed. A total of 36,000 genuine and relay attack transaction pairs were analysed using well-known machine learning algorithms. The results of our analysis indicate that the proposed solution is highly effective.

text: Good vibrations: artificial ambience-based relay attack detection Relay attacks are passive man in the middle attacks, aiming to extend the physical distance of devices involved in a transaction beyond their operating environment, within the restricted time-frame. In the field of smartphones, proposals have been put forward suggesting sensing the natural ambient environment as an effective Proximity and Relay Attack Detection (PRAD) mechanism. However, these proposals are not in compliance with industry imposed constraints (e.g. EMV and ITSO) mandating that transactions should complete within a certain time-frame (e.g. 500ms for EMV contactless transactions). The generation of an artificial ambient environment (AAE) using peripherals of the transaction devices has shown positive results when using infrared light as an AAE actuator. In this paper we propose the use of vibration as an alternative AAE actuator. We empirically evaluated the effectiveness of the proposed solution as a PRAD mechanism on an experimental test-bed that we deployed. A total of 36,000 genuine and relay attack transaction pairs were analysed using well-known machine learning algorithms. The results of our analysis indicate that the proposed solution is highly effective.

year: 2018

title: Riariakina ō rongo hirikapo From kōhanga reo to kura

authors: Hohepa, Margie Kahukura

abstract: Ko te kaupapa tonu, ko te whakatupu i te mahara o te hirikapo kia tiu ai ki te muri, arā, kia puta he whakaaro i pokepokengia nō roto tonu i ngā whakahekenga kāwai o ngā tūpuna o te tamaiti, kua maranga te wā e kaumātua haere ana te tamaiti, ngōna kanohi kua huaki, ngōna taringa kua pīkari, ngā whakaaro kua korikori, tōna wairua hīkaka kua ngawhā, ngērā kaupapa katoa o te tamaiti i taua wā o te tupu. Mā tēnei kōrero hoki hei kawe te taonga o te rongo hirikapo, arā, ngā whakaaro, ngā mahara, nāna ko te waha, nā te waha ko te kupu kōrero e makere iho ai i te ārero tarapepe. Heoi anō he tohutohu anō kei roto e kī ana, manaakingia ngā kai o te hirikapo o te tamaiti, he taonga. Ki te kore e tika te manaakingia e ngā mātua, tērā te wā ka ātitirauhea i te puāwaitanga o te rau. Ngērā kaupapa katoa. (Haki Tuaupiki, 2013)
This project grew out of the desire of a kōhanga and a kura—Te Kōhanga Reo o Ngā Kuaka and Tōku Māpihi Maurea Kura Kaupapa Māori respectively—to enhance transitions between their two sites for tamariki and whānau. Although visits to Tōku Māpihi Maurea before beginning at the kura were available for Ngā Kuaka tamariki on acceptance for enrolment, the instigators of this project believed a more formal transition programme would be beneficial to tamariki and their whānau. The kōhanga and kura were interested in tamariki and whānau experiencing a more effective transition across the two environments and the learning and curriculum in those respective sites.
The kōhanga and kura approached researchers at the University of Waikato Te Kura Toi Tangata Faculty of Education with the research question below and together we developed the proposal. From the outset the project was collaborative, cross-sector, and involved researchers from the kōhanga, the kura and the university.

text: Riariakina ō rongo hirikapo From kōhanga reo to kura Ko te kaupapa tonu, ko te whakatupu i te mahara o te hirikapo kia tiu ai ki te muri, arā, kia puta he whakaaro i pokepokengia nō roto tonu i ngā whakahekenga kāwai o ngā tūpuna o te tamaiti, kua maranga te wā e kaumātua haere ana te tamaiti, ngōna kanohi kua huaki, ngōna taringa kua pīkari, ngā whakaaro kua korikori, tōna wairua hīkaka kua ngawhā, ngērā kaupapa katoa o te tamaiti i taua wā o te tupu. Mā tēnei kōrero hoki hei kawe te taonga o te rongo hirikapo, arā, ngā whakaaro, ngā mahara, nāna ko te waha, nā te waha ko te kupu kōrero e makere iho ai i te ārero tarapepe. Heoi anō he tohutohu anō kei roto e kī ana, manaakingia ngā kai o te hirikapo o te tamaiti, he taonga. Ki te kore e tika te manaakingia e ngā mātua, tērā te wā ka ātitirauhea i te puāwaitanga o te rau. Ngērā kaupapa katoa. (Haki Tuaupiki, 2013)
This project grew out of the desire of a kōhanga and a kura—Te Kōhanga Reo o Ngā Kuaka and Tōku Māpihi Maurea Kura Kaupapa Māori respectively—to enhance transitions between their two sites for tamariki and whānau. Although visits to Tōku Māpihi Maurea before beginning at the kura were available for Ngā Kuaka tamariki on acceptance for enrolment, the instigators of this project believed a more formal transition programme would be beneficial to tamariki and their whānau. The kōhanga and kura were interested in tamariki and whānau experiencing a more effective transition across the two environments and the learning and curriculum in those respective sites.
The kōhanga and kura approached researchers at the University of Waikato Te Kura Toi Tangata Faculty of Education with the research question below and together we developed the proposal. From the outset the project was collaborative, cross-sector, and involved researchers from the kōhanga, the kura and the university.

year: 2017