How Fast Can We Play Tetris Greedily With Rectangular Pieces?

Consider a variant of Tetris played on a board of width $w$ and infinite height, where the pieces are axis-aligned rectangles of arbitrary integer dimensions, the pieces can only be moved before letting them drop, and a row does not disappear once it is full. Suppose we want to follow a greedy strategy: let each rectangle fall where it will end up the lowest given the current state of the board. To do so, we want a data structure which can always suggest a greedy move. In other words, we want a data structure which maintains a set of $O(n)$ rectangles, supports queries which return where to drop the rectangle, and updates which insert a rectangle dropped at a certain position and return the height of the highest point in the updated set of rectangles. We show via a reduction to the Multiphase problem [P\u{a}tra\c{s}cu, 2010] that on a board of width $w=\Theta(n)$, if the OMv conjecture [Henzinger et al., 2015] is true, then both operations cannot be supported in time $O(n^{1/2-\epsilon})$ simultaneously. The reduction also implies polynomial bounds from the 3-SUM conjecture and the APSP conjecture. On the other hand, we show that there is a data structure supporting both operations in $O(n^{1/2}\log^{3/2}n)$ time on boards of width $n^{O(1)}$, matching the lower bound up to a $n^{o(1)}$ factor.Comment: Correction of typos and other minor correction

Advanced Persistent Threats in Cybersecurity – Cyber Warfare

This book aims to provide a comprehensive analysis of Advanced Persistent Threats (APTs), including their characteristics, origins, methods, consequences, and defense strategies, with a focus on detecting these threats. It explores the concept of advanced persistent threats in the context of cyber security and cyber warfare. APTs represent one of the most insidious and challenging forms of cyber threats, characterized by their sophistication, persistence, and targeted nature. The paper examines the origins, characteristics and methods used by APT actors. It also explores the complexities associated with APT detection, analyzing the evolving tactics used by threat actors and the corresponding advances in detection methodologies. It highlights the importance of a multi-faceted approach that integrates technological innovations with proactive defense strategies to effectively identify and mitigate APT

On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

NASA Langley Scientific and Technical Information Output: 1998

This document is a compilation of the scientific and technical information that the Langley Research Center has produced during the calendar year 1998. Included are citations for Technical Publications, Conference Publications, Technical Memorandums, Contractor Reports, Journal Articles and Book Publications, Meeting Presentations, Technical Talks, and Patents

Tree comparison: enumeration and application to cheminformatics

Graphs are a well-known data structure used in many application domains that rely on relationships between individual entities. Examples are social networks, where the users may be in friendship with each other, road networks, where one-way or bidirectional roads connect crossings, and work package assignments, where workers are assigned to tasks. In chem- and bioinformatics, molecules are often represented as molecular graphs, where vertices represent atoms, and bonds between them are represented by edges connecting the vertices. Since there is an ever-increasing amount of data that can be treated as graphs, fast algorithms are needed to compare such graphs. A well-researched concept to compare two graphs is the maximum common subgraph. On the one hand, this allows finding substructures that are common to both input graphs. On the other hand, we can derive a similarity score from the maximum common subgraph. A practical application is rational drug design which involves molecular similarity searches. In this thesis, we study the maximum common subgraph problem, which entails finding a largest graph, which is isomorphic to subgraphs of two input graphs. We focus on restrictions that allow polynomial-time algorithms with a low exponent. An example is the maximum common subtree of two input trees. We succeed in improving the previously best-known time bound. Additionally, we provide a lower time bound under certain assumptions. We study a generalization of the maximum common subtree problem, the block-and-bridge preserving maximum common induced subgraph problem between outerplanar graphs. This problem is motivated by the application to cheminformatics. First, the vast majority of drugs modeled as molecular graphs is outerplanar, and second, the blocks correspond to the ring structures and the bridges to atom chains or linkers. If we allow disconnected common subgraphs, the problem becomes NP-hard even for trees as input. We propose a second generalization of the maximum common subtree problem, which allows skipping vertices in the input trees while maintaining polynomial running time. Since a maximum common subgraph is not unique in general, we investigate the problem to enumerate all maximum solutions. We do this for both the maximum common subtree problem and the block-and-bridge preserving maximum common induced subgraph problem between outerplanar graphs. An arising subproblem which we analyze is the enumeration of maximum weight matchings in bipartite graphs. We support a weight function between the vertices and edges for all proposed common subgraph methods in this thesis. Thus the objective is to compute a common subgraph of maximum weight. The weights may be integral or real-valued, including negative values. A special case of using such a weight function is computing common subgraph isomorphisms between labeled graphs, where labels between mapped vertices and edges must be equal. An experimental study evaluates the practical running times and the usefulness of our block-and-bridge preserving maximum common induced subgraph algorithm against state of the art algorithms

The Encyclopedia of Neutrosophic Researchers - vol. 1

This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining significant attention in solving many real life problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistent, and indeterminacy. In the past years the fields of neutrosophics have been extended and applied in various fields, such as: artificial intelligence, data mining, soft computing, decision making in incomplete / indeterminate / inconsistent information systems, image processing, computational modelling, robotics, medical diagnosis, biomedical engineering, investment problems, economic forecasting, social science, humanistic and practical achievements

A Universal Knowledge Model and Cognitive Architecture for Prototyping AGI

The article identified 42 cognitive architectures for creating general artificial intelligence (AGI) and proposed a set of interrelated functional blocks that an agent approaching AGI in its capabilities should possess. Since the required set of blocks is not found in any of the existing architectures, the article proposes a new cognitive architecture for intelligent systems approaching AGI in their capabilities. As one of the key solutions within the framework of the architecture, a universal method of knowledge representation is proposed, which allows combining various non-formalized, partially and fully formalized methods of knowledge representation in a single knowledge base, such as texts in natural languages, images, audio and video recordings, graphs, algorithms, databases, neural networks, knowledge graphs, ontologies, frames, essence-property-relation models, production systems, predicate calculus models, conceptual models, and others. To combine and structure various fragments of knowledge, archigraph models are used, constructed as a development of annotated metagraphs. As components, the cognitive architecture being developed includes machine consciousness, machine subconsciousness, blocks of interaction with the external environment, a goal management block, an emotional control system, a block of social interaction, a block of reflection, an ethics block and a worldview block, a learning block, a monitoring block, blocks of statement and solving problems, self-organization and meta learning block