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## Cascade Heap: Towards Time-Optimal Extractions

Heaps are well-studied fundamental data structures, having myriads of applications, both theoretical and practical. We consider the problem of designing a heap with an “optimal” extract-min operation. Assuming an arbitrary linear ordering of keys, a heap with n elements typically takes O(log n) time to extract the minimum. Extracting all elements faster is impossible as this would violate the Ω (nlog n) bound for comparison-based sorting. It is known, however, that is takes only O(n+ klog k) time to sort just k smallest elements out of n given, which prompts that there might be a faster heap, whose extract-min performance depends on the number of elements extracted so far. In this paper we show that this is indeed the case. We present a version of heap that performs insert in O(1) time and takes only O(log ∗ n+ log k) time to carry out the k-th extraction (where log ∗ denotes the iterated logarithm). All the above bounds are worst-case. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

The article discusses issues related to computer science and programming teaching for undergraduate students of universities and collegues. Enrollee's classification and expected learning outcomes are included. Every discipline included in Computer Science course is also described in details

Special issue of Elsevier’s Procedia Computer Science, which consists of the proceedings of the 20th International Conference on Knowledge - Based and Intelligent Information & Engineering Systems (KES2016) which was organised by KES International and held on September 5th to 7th, 2016 in York, United Kingdom. Celebrating 20 years of KES conferences, KES2016 was the 20th event in a series of broad-spectrum intelligent systems conferences first held in Adelaide, Australia in 1997. The main aim of this KES conference series is to provide an internationally respected forum for the dissemination of research results and the discussion of issues relating to the theory, technologies and applications of intelligent information and knowledge-based systems. This year, this truly international conference attracted a substantial number of researchers and practitioners from all over the world who submitted their papers to five general tracks and 28 special sessions on specific topics. The papers highlight the new trends and challenge of intelligent and knowledge-based systems. Each paper was peer reviewed by at least two members of the International Program Committee and International Reviewer Board. Out of a large number of submissions, more than 200 high-quality papers were accepted for oral presentation and publication in Procedia Computer Science, submitted for indexing in CPCi (ISI conferences), Engineering Index, and Scopus.

In their seminal paper:

Lincoln, P., Mitchell, J., Scedrov, A. and Shankar, N. (1992). Decision problems for propositional linear logic. Annals of Pure and Applied Logic 56 (1–3) 239–311,

LMSS have established an extremely surprising result that propositional linear logic is undecidable. Their proof is very complex and involves numerous nested inductions of different kinds. Later an alternative proof for the LL undecidability has been developed based on simulation Minsky machines in linear logic: Kanovich, M. (1995). The direct simulation of Minsky machines in linear logic. In: Girard, J.-Y., Lafont, Y. and Regnier, L. (eds.) Advances in Linear Logic, London Mathematical Society Lecture Notes, volume 222, Cambridge University Press 123–145. Notice that this direct simulation approach has been successfully applied for a large number of formal systems with resolving a number of open problems in computer science and even computational linguistics, e.g.,

James Brotherston, Max I. Kanovich: Undecidability of Propositional Separation Logic and Its Neighbours. J. ACM 61(2): 14:1-14:43 (2014), Max Kanovich, Stepan Kuznetsov, Andre Scedrov: Undecidability of the Lambek Calculus with a Relevant Modality. FG 2016: 240-256. Nevertheless, recently the undecidability of linear logic is questioned by some people. They claim that they have found lacunae in the LMSS 1992 paper, and, moreover, they have a proof that propositional linear logic is decidable!!! I have been asked to submit a paper, as clear as possible, to the Journal, in order to sort out such a confusing problem, once and for all.

Here, we give a fully self-contained, easy-to-follow, but fully detailed, direct and constructive proof of the undecidability of a very simple Horn-like fragment of linear logic, the proof is accessible to a wide range of people. Namely, we show that there is a direct correspondence between terminated computations of a Minsky machine M and cut-free linear logic derivations for a Horn-like sequent of the form \Phi_M, l1 |- l0 where \Phi_M consists only of Horn-like implications of the very simple forms. Neither negation, nor &, nor constants, nor embedded implications/bangs are used here. Furthermore, our particular correspondence constructed above provides decidability for some smaller Horn-like fragments along with the complexity bounds that come from the proof.

This book constitutes the refereed proceedings of the 23rd Annual Symposium on Combinatorial Pattern Matching, CPM 2012, held in Helsinki, Finalnd, in July 2012. The 33 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 60 submissions. The papers address issues of searching and matching strings and more complicated patterns such as trees, regular expressions, graphs, point sets, and arrays. The goal is to derive non-trivial combinatorial properties of such structures and to exploit these properties in order to either achieve superior performance for the corresponding computational problems or pinpoint conditions under which searches cannot be performed efficiently. The meeting also deals with problems in computational biology, data compression and data mining, coding, information retrieval, natural language processing, and pattern recognition.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.