587 research outputs found
New Type of Coding Problem Motivated by Database Theory
The present paper is intended to survey the interaction between relational database theory and coding theory. In particular it is shown how an extremal problem for relational databases gives rise to a new type of coding problem. The former concerns minimal representation of branching dependencies that can be considered as a data mining type question. The extremal configurations involve d-distance sets in the space of disjoint pairs of k-element subsets of an n-element set X. Let X be an n-element finite set, 0 < k < n/2 an integer. Suppose that {A(1), B-1} and {A(2), B-2} are pairs of disjoint k-element subsets of X (that is, \A(1)\ = \B-1\ = \A(2)\ = \B-2\ = k, A(1) boolean AND B-1 = 0, A(2) boolean AND B-2 = 0). Define the distance of these pairs by d({A(1), B-1}, {A(2), B-2}) = min{\A(1) - A(2)\ + \B-1 - B-2\, \A(1) - B-2\ + \B-1 - A(2)\). (C) 2004 Elsevier B.V. All rights reserved
Rectangular Layouts and Contact Graphs
Contact graphs of isothetic rectangles unify many concepts from applications
including VLSI and architectural design, computational geometry, and GIS.
Minimizing the area of their corresponding {\em rectangular layouts} is a key
problem. We study the area-optimization problem and show that it is NP-hard to
find a minimum-area rectangular layout of a given contact graph. We present
O(n)-time algorithms that construct -area rectangular layouts for
general contact graphs and -area rectangular layouts for trees.
(For trees, this is an -approximation algorithm.) We also present an
infinite family of graphs (rsp., trees) that require (rsp.,
) area.
We derive these results by presenting a new characterization of graphs that
admit rectangular layouts using the related concept of {\em rectangular duals}.
A corollary to our results relates the class of graphs that admit rectangular
layouts to {\em rectangle of influence drawings}.Comment: 28 pages, 13 figures, 55 references, 1 appendi
Relation-algebraic modeling and solution of chessboard independence and domination problems
AbstractWe describe a simple computing technique for solving independence and domination problems on rectangular chessboards. It rests upon relational modeling and uses the BDD-based specific purpose computer algebra system RelView for the evaluation of the relation-algebraic expressions that specify the problems’ solutions and the visualization of the computed results. The technique described in the paper is very flexible and especially appropriate for experimentation. It can easily be applied to other chessboard problems
Introducing LambdaTensor1.0 - A package for explicit symbolic and numeric Lie algebra and Lie group calculations
Due to the occurrence of large exceptional Lie groups in supergravity, calculations involving explicit Lie algebra and Lie group element manipulations easily become very complicated and hence also error-prone if done by hand. Research on the extremal structure of maximal gauged supergravity theories in various dimensions sparked the development of a library for efficient abstract multilinear algebra calculations involving sparse and non-sparse higher-rank tensors, which is presented here
Recent Conceptual Consequences of Loop Quantum Gravity. Part I: Foundational Aspects
Conceptual consequences of recent results in loop quantum gravity are
collected and discussed here in view of their implications for a modern
philosophy of science which is mainly understood as one that totalizes
scientific insight so as to eventually achieve a consistent model of what may
be called fundamental heuristics on an onto-epistemic background which is part
of recently proposed transcendental materialism. This enterprise is being
understood as a serious attempt of answering recent appeals to philosophy so as
to provide a conceptual foundation for what is going on in modern physics, and
of bridging the obvious gap between physics and philosophy. This present first
part of the paper deals with foundational aspects of this enterprise, a second
part will deal with its holistic aspects.Comment: 25 page
Decision-making and problem-solving methods in automation technology
The state of the art in the automation of decision making and problem solving is reviewed. The information upon which the report is based was derived from literature searches, visits to university and government laboratories performing basic research in the area, and a 1980 Langley Research Center sponsored conferences on the subject. It is the contention of the authors that the technology in this area is being generated by research primarily in the three disciplines of Artificial Intelligence, Control Theory, and Operations Research. Under the assumption that the state of the art in decision making and problem solving is reflected in the problems being solved, specific problems and methods of their solution are often discussed to elucidate particular aspects of the subject. Synopses of the following major topic areas comprise most of the report: (1) detection and recognition; (2) planning; and scheduling; (3) learning; (4) theorem proving; (5) distributed systems; (6) knowledge bases; (7) search; (8) heuristics; and (9) evolutionary programming
Perfect error-correcting databases
AbstractAn n×m matrix is called a t-error-correcting database if after deleting any t columns one can still distinguish the rows. It is perfect if after omitting any t+1 columns two identical rows are obtained. (Stating with another terminology, the system of minimal keys induced by A is the system of all (n−t)-element subsets of an n-element set.)Let ft(n) denote the minimum number of rows in a perfect t-error-correcting database of length n. We show that f2(n)=Θ(n2), and in general Ω(n(2t+1)⧸3)≤ft(n)≤O(nt) for t≥3, whenever n→∞
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