Strengthened Lazy Heaps: Surpassing the Lower Bounds for Binary Heaps

Let $n$ denote the number of elements currently in a data structure. An in-place heap is stored in the first $n$ locations of an array, uses $O(1)$ extra space, and supports the operations: minimum, insert, and extract-min. We introduce an in-place heap, for which minimum and insert take $O(1)$ worst-case time, and extract-min takes $O(\lg{} n)$ worst-case time and involves at most $\lg{} n + O(1)$ element comparisons. The achieved bounds are optimal to within additive constant terms for the number of element comparisons. In particular, these bounds for both insert and extract-min -and the time bound for insert- surpass the corresponding lower bounds known for binary heaps, though our data structure is similar. In a binary heap, when viewed as a nearly complete binary tree, every node other than the root obeys the heap property, i.e. the element at a node is not smaller than that at its parent. To surpass the lower bound for extract-min, we reinforce a stronger property at the bottom levels of the heap that the element at any right child is not smaller than that at its left sibling. To surpass the lower bound for insert, we buffer insertions and allow $O(\lg^2{} n)$ nodes to violate heap order in relation to their parents

Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls

We consider space-bounded computations on a random-access machine (RAM) where the input is given on a read-only random-access medium, the output is to be produced to a write-only sequential-access medium, and the available workspace allows random reads and writes but is of limited capacity. The length of the input is $N$ elements, the length of the output is limited by the computation, and the capacity of the workspace is $O(S)$ bits for some predetermined parameter $S$. We present a state-of-the-art priority queue---called an adjustable navigation pile---for this restricted RAM model. Under some reasonable assumptions, our priority queue supports $\mathit{minimum}$ and $\mathit{insert}$ in $O(1)$ worst-case time and $\mathit{extract}$ in $O(N/S + \lg{} S)$ worst-case time for any $S \geq \lg{} N$. We show how to use this data structure to sort $N$ elements and to compute the convex hull of $N$ points in the two-dimensional Euclidean space in $O(N^2/S + N \lg{} S)$ worst-case time for any $S \geq \lg{} N$. Following a known lower bound for the space-time product of any branching program for finding unique elements, both our sorting and convex-hull algorithms are optimal. The adjustable navigation pile has turned out to be useful when designing other space-efficient algorithms, and we expect that it will find its way to yet other applications.Comment: 21 page

Finance-Growth Nexus and Convergence

This thesis revises the relationship between financial development and the economic growth, the finance-growth nexus. This thesis expands the existing literature by using more sophisticated measures to determine the level of financial development to get a more accurate impression on the effect it has on economic growth. Economic growth has been a constant long-term trend in the recorded economic history. It can be decomposed to three elements: growth in labour, capital stock, and the total factor of productivity (TFP). The financial sector is mainly able to affect growth through the TFP, although it also plays a central role in enabling investment and thus growing the capital stock of the economy. The primary function of the financial sector is to allocate the society's resources efficiently under uncertainty. It does so by performing its five basic functions: risk management, transfer of economic resources, corporate control, mobilization of savings, and facilitation of exchange. I find that all benchmark variables describing financial development have got an effect on economic growth and convergence, depending on the situation and the type of examination. None of the variables show a consistent dominating effect, which supports using the variables as a group instead of solely relying on one of the selected variables.fi=Opinnäytetyö kokotekstinä PDF-muodossa.|en=Thesis fulltext in PDF format.|sv=Lärdomsprov tillgängligt som fulltext i PDF-format

Priority queues and sorting for read-only data

Abstract. We revisit the random-access-machine model in which the input is given on a read-only random-access media, the output is to be produced to a write-only sequential-access media, and in addition there is a limited random-access workspace. The length of the input is N elements, the length of the output is limited by the computation itself, and the capacity of the workspace is O(S + w) bits, where S is a parameter specified by the user and w is the number of bits per machine word. We present a state-of-the-art priority queue-called an adjustable navigation pile-for this model. Under some reasonable assumptions, our priority queue supports minimum and insert in O(1) worst-case time and extract in O(N/S +lg S) worst-case time, where lg N ≤ S ≤ N/ lg N . We also show how to use this data structure to simplify the existing optimal O(N 2 /S + N lg S)-time sorting algorithm for this model

Learning with Knowledge Sharing in Social Networks

Working in the digitally networked world has become more complex and dynamic. We need new ways of learning in order to adapt information and knowledge surrounding us. Our information seeking and media habits are relying heavily on web-supported services. Informal and networked work has become as important as the formal work. Social media has become the center of communities where projects, learning, collaboration, information sharing and training are created. Social media engages employees to capture and share knowledge in ways that has not been possible before with formal learning. Web has also become a learning environment where understanding is socially shared. The place where learning is shared also creates usually new knowledge. Knowledge creation in organization can be seen as a continuous and dynamic process, where tacit knowledge is the most valuable competitive asset of an organization. Social web enables new ways of learning and knowledge creation for the entire organization and future employee generations. The main goal of this research is to research how quality criteria of learning in social network is achieved and potentially adapted to organizations. Learning in a company has shifted more towards situated learning were communication cannot be necessary done physically between employees. The benefits of using online learning are for example increased access, more learner centralized processes, better decision-making and cost-effectiveness. New technologies and the need for globalization are quickly making distributed communities of practice a standard practice of a learning organization. Online communities have become global and the physical distance between community learners is not that crucial anymore. The focus of this research is to find out how an organization uses social media in their internal learning purposes like keeping up to date with industry, organizational networking, team collaboration and social training. Online communities with social networking can be seen as modern day communities of practice. Social networking provides multiple ways of collaborating in synchronous and asynchronous processes. It supports keeping information current, creates systems that support updates and sharing of collective perspectives. Emerging web technologies in communities allow us to create dialogues inside and outside the community. Google+ social networking service is one of the few social networking services that support versatile communications and potentially variety different learning ways. Google has been the most dominant player of the most popular Internet services. Google+ is a new social networking service, which provides a variety of tools for collaboration, good usability, and different connections methods with a social environment. It also builds a network where knowledge sharing is easily encouraged between users and groups of people. The amount of information is overwhelming for individual learners to adopt and process. For information seeking, problem solving and understanding complexity we need collaborative tools to support our ways of learning. Lack of recognizing the change in learning and learning environments can lead to bad decisions and inefficient processes. Online learning can enable and make information spread effectively by recommendations, automatic preferences, community tools and information filters. All of the above help learners to focus on the most crucial and specified information needed for succeeding in every day work. Social networking for learning purposes and its internal organizational use has been used and researched limitedly. This research seeks to apply a conceptual framework of learning organization concept. After describing the concept I will qualitatively test Google + social network’s suitability for supporting learning in organizational setting and draw an assessment based on these results. This thesis work is an interdisciplinary research representing theories and practices from pedagogy, psychology, sociology, economics and technology

Heaps and heapsort on secondary storage

AbstractA heap structure designed for secondary storage is suggested that tries to make the best use of the available buffer space in primary memory. The heap is a complete multi-way tree, with multi-page blocks of records as nodes, satisfying a generalized heap property. A special feature of the tree is that the nodes may be partially filled, as in B-trees. The structure is complemented with priority-queue operations insert and delete-max. When handling a sequence of S operations, the number of page transfers performed is shown to be O(∑i = 1S(1P) log(MP)(NiP)), where P denotes the number of records fitting into a page, M the capacity of the buffer space in records, and Ni, the number of records in the heap prior to the ith operation (assuming P ⩾ 1 and S > M ⩾ c · P, where c is a small positive constant). The number of comparisons required when handling the sequence is O(∑i = 1S log2 Ni). Using the suggested data structure we obtain an optimal external heapsort that performs O((NP) log(MP)(NP)) page transfers and O(N log2 N) comparisons in the worst case when sorting N records

The Open Graph Archive: A Community-Driven Effort

In order to evaluate, compare, and tune graph algorithms, experiments on well designed benchmark sets have to be performed. Together with the goal of reproducibility of experimental results, this creates a demand for a public archive to gather and store graph instances. Such an archive would ideally allow annotation of instances or sets of graphs with additional information like graph properties and references to the respective experiments and results. Here we examine the requirements, and introduce a new community project with the aim of producing an easily accessible library of graphs. Through successful community involvement, it is expected that the archive will contain a representative selection of both real-world and generated graph instances, covering significant application areas as well as interesting classes of graphs.Comment: 10 page