On Minimum Maximal Distance-k Matchings

We study the computational complexity of several problems connected with finding a maximal distance-$k$ matching of minimum cardinality or minimum weight in a given graph. We introduce the class of $k$-equimatchable graphs which is an edge analogue of $k$-equipackable graphs. We prove that the recognition of $k$-equimatchable graphs is co-NP-complete for any fixed $k \ge 2$. We provide a simple characterization for the class of strongly chordal graphs with equal $k$-packing and $k$-domination numbers. We also prove that for any fixed integer $\ell \ge 1$ the problem of finding a minimum weight maximal distance-$2\ell$ matching and the problem of finding a minimum weight $(2 \ell - 1)$-independent dominating set cannot be approximated in polynomial time in chordal graphs within a factor of $\delta \ln |V(G)|$ unless $\mathrm{P} = \mathrm{NP}$, where $\delta$ is a fixed constant (thereby improving the NP-hardness result of Chang for the independent domination case). Finally, we show the NP-hardness of the minimum maximal induced matching and independent dominating set problems in large-girth planar graphs.Comment: 15 pages, 4 figure

On Existential MSO and its Relation to ETH

Impagliazzo et al. proposed a framework, based on the logic fragment defining the complexity class SNP, to identify problems that are equivalent to k-CNF-Sat modulo subexponential-time reducibility (serf-reducibility). The subexponential-time solvability of any of these problems implies the failure of the Exponential Time Hypothesis (ETH). In this paper, we extend the framework of Impagliazzo et al., and identify a larger set of problems that are equivalent to k-CNF-Sat modulo serf-reducibility. We propose a complexity class, referred to as Linear Monadic NP, that consists of all problems expressible in existential monadic second order logic whose expressions have a linear measure in terms of a complexity parameter, which is usually the universe size of the problem. This research direction can be traced back to Fagin\u27s celebrated theorem stating that NP coincides with the class of problems expressible in existential second order logic. Monadic NP, a well-studied class in the literature, is the restriction of the aforementioned logic fragment to existential monadic second order logic. The proposed class Linear Monadic NP is then the restriction of Monadic NP to problems whose expressions have linear measure in the complexity parameter. We show that Linear Monadic NP includes many natural complete problems such as the satisfiability of linear-size circuits, dominating set, independent dominating set, and perfect code. Therefore, for any of these problems, its subexponential-time solvability is equivalent to the failure of ETH. We prove, using logic games, that the aforementioned problems are inexpressible in the monadic fragment of SNP, and hence, are not captured by the framework of Impagliazzo et al. Finally, we show that Feedback Vertex Set is inexpressible in existential monadic second order logic, and hence is not in Linear Monadic NP, and investigate the existence of certain reductions between Feedback Vertex Set (and variants of it) and 3-CNF-Sat

Air Force Institute of Technology Research Report 2009

This report summarizes the research activities of the Air Force Institute of Technology’s Graduate School of Engineering and Management. It describes research interests and faculty expertise; lists student theses/dissertations; identifies research sponsors and contributions; and outlines the procedures for contacting the school. Included in the report are: faculty publications, conference presentations, consultations, and funded research projects. Research was conducted in the areas of Aeronautical and Astronautical Engineering, Electrical Engineering and Electro-Optics, Computer Engineering and Computer Science, Systems and Engineering Management, Operational Sciences, Mathematics, Statistics and Engineering Physics

The complexity of approximately counting in 2-spin systems on kk-uniform bounded-degree hypergraphs

One of the most important recent developments in the complexity of approximate counting is the classification of the complexity of approximating the partition functions of antiferromagnetic 2-spin systems on bounded-degree graphs. This classification is based on a beautiful connection to the so-called uniqueness phase transition from statistical physics on the infinite $\Delta$-regular tree. Our objective is to study the impact of this classification on unweighted 2-spin models on $k$-uniform hypergraphs. As has already been indicated by Yin and Zhao, the connection between the uniqueness phase transition and the complexity of approximate counting breaks down in the hypergraph setting. Nevertheless, we show that for every non-trivial symmetric $k$-ary Boolean function $f$ there exists a degree bound $\Delta_0$ so that for all $\Delta \geq \Delta_0$ the following problem is NP-hard: given a $k$-uniform hypergraph with maximum degree at most $\Delta$, approximate the partition function of the hypergraph 2-spin model associated with $f$. It is NP-hard to approximate this partition function even within an exponential factor. By contrast, if $f$ is a trivial symmetric Boolean function (e.g., any function $f$ that is excluded from our result), then the partition function of the corresponding hypergraph 2-spin model can be computed exactly in polynomial time

A User-aware Intelligent Refactoring for Discrete and Continuous Software Integration

Successful software products evolve through a process of continual change. However, this process may weaken the design of the software and make it unnecessarily complex, leading to significantly reduced productivity and increased fault-proneness. Refactoring improves the software design while preserving overall functionality and behavior, and is an important technique in managing the growing complexity of software systems. Most of the existing work on software refactoring uses either an entirely manual or a fully automated approach. Manual refactoring is time-consuming, error-prone and unsuitable for large-scale, radical refactoring. Furthermore, fully automated refactoring yields a static list of refactorings which, when applied, leads to a new and often hard to comprehend design. In addition, it is challenging to merge these refactorings with other changes performed in parallel by developers. In this thesis, we propose a refactoring recommendation approach that dynamically adapts and interactively suggests refactorings to developers and takes their feedback into consideration. Our approach uses Non-dominated Sorting Genetic Algorithm (NSGAII) to find a set of good refactoring solutions that improve software quality while minimizing the deviation from the initial design. These refactoring solutions are then analyzed to extract interesting common features between them such as the frequently occurring refactorings in the best non-dominated solutions. We combined our interactive approach and unsupervised learning to reduce the developer’s interaction effort when refactoring a system. The unsupervised learning algorithm clusters the different trade-off solutions, called the Pareto front, to guide the developers in selecting their region of interests and reduce the number of refactoring options to explore. To reduce the interaction effort, we propose an approach to convert multi-objective search into a mono-objective one after interacting with the developer to identify a good refactoring solution based on their preferences. Since developers may want to focus on specific code locations, the ”Decision Space” is also important. Therefore, our interactive approach enables developers to pinpoint their preference simultaneously in the objective (quality metrics) and decision (code location) spaces. Due to an urgent need for refactoring tools that can support continuous integration and some recent development processes such as DevOps that are based on rapid releases, we propose, for the first time, an intelligent software refactoring bot, called RefBot. Our bot continuously monitors the software repository and find the best sequence of refactorings to fix the quality issues in Continous Integration/Continous Development (CI/CD) environments as a set of pull-requests generated after mining previous code changes to understand the profile of developers. We quantitatively and qualitatively evaluated the performance and effectiveness of our proposed approaches via a set of studies conducted with experienced developers who used our tools on both open source and industry projects.Ph.D.College of Engineering & Computer ScienceUniversity of Michigan-Dearbornhttps://deepblue.lib.umich.edu/bitstream/2027.42/154775/1/Vahid Alizadeh Final Dissertation.pdfDescription of Vahid Alizadeh Final Dissertation.pdf : Dissertatio

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

6. Uluslararası Öğrenciler Fen Bilimleri Kongresi: Tam Metin Bildiriler Kitabı, 20-21 Mayıs 2022

Çevrimiçi (X, 434 Sayfa; 26 cm.)Değerli Katılımcılar, Meslektaşlarım ve Uluslararası Öğrenciler, 6. Uluslararası Öğrenciler Fen Bilimleri Kongresi Tam metin Kitabını etkinliğin yazarlarına ve katılımcılarına sunmak bizler için büyük bir onur ve ayrıcalıktır. Bunu yararlı, heyecan ve ilham verici bulacağınızı umuyoruz. Son beş yıldır çeşitli bilim dallarında çalışan genç uluslararası araştırmacıları bir araya getirmek amacıyla kongrelerimizi düzenledik ve bu hepimizi gerçekten motive etti. Küresel Covid-19 pandemisinin ardından altıncı kongreyi, yüz yüze canlı ve çevrimiçi sanal oturumları birleştirerek karma bir etkinlik olarak düzenledik. Kongrenin ilk günü olan 20 Mayıs’ta, 100'den fazla katılımcıyı bir araya getiren ve tamamen yüz yüze sekiz oturum gerçekleştirildi. Bu ilk günün sabahında davetli konuşmacılarımız tarafından iki ilgi çekici sunum yapıldı: Ege Üniversitesi'nden Prof. Dr. Bahattin Tanyolaç “Covid-19 Aşıları” ve Gebze Teknik Üniversitesi'nden Dr. Yakup Genç “Metaverse” hakkında konuştular. Etkinliğin ikinci gününde dokuz çevrimiçi oturum Zoom üzerinden gerçekleştirildi ve YouTube üzerinden canlı olarak yayınlandı; bu oturumların videolarına Youtube kanalımızdan ulaşabilirsiniz. Altıncı kongremizi de yine büyük bir istek ve heyecanla gerçekleştirdik. İki gün süren kongrede, yirmi sekiz farklı ülkeden yüz elliyi aşkın genç araştırmacı ve akademisyen bir araya geldi ve on yedi oturumda toplam doksan yedi bildiri sunuldu. Bildirilerin kırk yedi tanesi canlı yüz yüze, elli tanesi ise çevrimiçi olarak sunuldu. Öte yandan, elli iki bildiri uluslararası (Türk olmayan) katılımcılar tarafından, kırk beş bildiri ise Türk katılımcılar tarafından sunuldu. Kongre, özellikle fen bilimleri alanında eğitimlerine devam eden uluslararası öğrencilerin ve genç akademisyenlerin önlerindeki akademik camia ile etkileşimlerini gayet samimi bir ortam sunarak teşvik ederken, yeni ve güncel çalışmalarını sunmaları ve tartışmaları için de güzel bir fırsat sağlamış oldu. Onların katkıları sayesinde Kongre olabildiğince seçkin ve nitelikli bir düzeye ulaşmış oldu. Kongre, Ziraat Mühendisliği, Mimarlık, Biyoloji ve Biyomühendislik, Kimya ve Kimya Mühendisliği, İnşaat Mühendisliği, Bilgisayar Bilimi ve Mühendisliği, Elektrik, Elektronik ve Haberleşme Mühendisliği, Enerji, Gıda Mühendisliği, Jeoloji Mühendisliği, Makine Mühendisliği, Matematik, Malzeme Bilimi, Metalürji ve Malzeme Mühendisliği, Mekatronik Mühendisliği, Nanoteknoloji, Fizik, Tekstil Mühendisliği, Kentsel ve Bölgesel Planlama, vb. çok çeşitli konulardaki son gelişmeleri tartışmak için keyifli bir ortam sağladı. Tüm katılımcılara kongre programımıza ve dolayısıyla tam metin kitabımıza yaptıkları katkılardan dolayı teşekkür ederiz. Ayrıca verdikleri destek ile bu kongrenin gerçekleşmesine katkı sağlayan İzmir Kâtip Çelebi Üniversitesi’ne, Uluslararası Öğrenci Dernekleri Federasyonu’na (UDEF), Türkiye Bilimsel ve Teknolojik Araştırma Kurumu’na (TÜBİTAK) ve ana organizatörümüz İzmir Uluslararası Misafir Öğrenci Derneği'ne teşekkürlerimizi arz ederiz. Organizasyon komitemize ve etkinlik süresince gönüllü olarak çalışan tüm öğrencilere içten şükran ve takdirlerimi sunuyorum. Bu kongre dizisinin devam eden başarısı, 2023'te düzenlenmeyi hedeflediğimiz 7. Uluslararası Öğrenciler Fen Bilimleri Kongresi için planlamanın artık güvenle ilerleyebileceği anlamına geliyor; bu kongremiz de muhtemelen hem çevrimiçi hem de yüz yüze olacak. Katkılarından dolayı tüm yazarlara, katılımcılara ve gönüllülere teşekkür ederiz. Prof. Dr. Mehmet Çevik Kongre Başkan