Showing papers on "Disjoint sets published in 2002"

Wireless Sensor Networks with Energy Efficient Organization

Abstract: A critical aspect of applications with wireless sensor networks is network lifetime. Battery-powered sensors are usable as long as they can communicate captured data to a processing node. Sensing and communications consume energy, therefore judicious power management and scheduling can effectively extend the operational time. One important class of wireless sensor applications of deployment of large number of sensors in an area for environmental monitoring. The data collected by the sensors is sent to a central node for processing. In this paper we propose an efficient method to achieve energy savings by organizing the sensor nodes into a maximum number of disjoint dominating sets (DDS) which are activated successively. Only the sensors from the active set are responsible for monitoring the target area and for disseminating the collected data. All other nodes are into a sleep mode, characterized by a low energy consumption. We define the maximum disjoint dominating sets problem and we design a heuristic that computes the sets. Theoretical analysis and performance evaluation results are presented to verify our approach.

Kneser's Conjecture

Abstract: A combinatorial conjecture formulated by Kneser (1955). It states that whenever the n-subsets of a (2n+k)-set are divided into k+1 classes, then two disjoint subsets end up in the same class. Lovasz (1978) gave a proof based on graph theory. In particular, he showed that the Kneser graph, whose vertices represent the n-subsets, and where each edge connects two disjoint subsets, is not (k+1)-colorable. More precisely, his results says that the chromatic number is equal to k+2, and this...

Quantum lower bound for the collision problem

Abstract: (MATH) The collision problem is to decide whether a function X: { 1,…,n} → { 1, …,n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of Ω(n1/5) on the number of queries needed by a quantum computer to solve this problem with bounded error probability. The best known upper bound is O(n1/3), but obtaining any lower bound better than Ω(1) was an open problem since 1997. Our proof uses the polynomial method augmented by some new ideas. We also give a lower bound of Ω(n1/7) for the problem of deciding whether two sets are equal or disjoint on a constant fraction of elements. Finally we give implications of these results for quantum complexity theory.

A Spatial Logic for Querying Graphs

Abstract: We study a spatial logic for reasoning about labelled directed graphs, and the application of this logic to provide a query language for analysing and manipulating such graphs. We give a graph description using constructs from process algebra. We introduce a spatial logic in order to reason locally about disjoint subgraphs. We extend our logic to provide a query language which preserves the multiset semantics of our graph model. Our approach contrasts with the more traditional set-based semantics found in query languages such as TQL, Strudel and GraphLog.

A disjoint path selection scheme with shared risk link groups in GMPLS networks

Abstract: This letter proposes a disjoint path selection scheme for generalized multi-protocol label switching (GMPLS) networks with shared risk link group (SRLG) constraints. It is called the weighted-SRLG (WSRLG) scheme. It treats the number of SRLG members related to a link as part of the link cost when the k-shortest path algorithm is executed. In WSRLG, a link that has many SRLG members is rarely selected as the shortest path. Simulation results show that WSRLG finds more disjoint paths than the conventional k-shortest path algorithm.

Boosting Algorithms for Parallel and Distributed Learning

Abstract: The growing amount of available information and its distributed and heterogeneous nature has a major impact on the field of data mining. In this paper, we propose a framework for parallel and distributed boosting algorithms intended for efficient integrating specialized classifiers learned over very large, distributed and possibly heterogeneous databases that cannot fit into main computer memory. Boosting is a popular technique for constructing highly accurate classifier ensembles, where the classifiers are trained serially, with the weights on the training instances adaptively set according to the performance of previous classifiers. Our parallel boosting algorithm is designed for tightly coupled shared memory systems with a small number of processors, with an objective of achieving the maximal prediction accuracy in fewer iterations than boosting on a single processor. After all processors learn classifiers in parallel at each boosting round, they are combined according to the confidence of their prediction. Our distributed boosting algorithm is proposed primarily for learning from several disjoint data sites when the data cannot be merged together, although it can also be used for parallel learning where a massive data set is partitioned into several disjoint subsets for a more efficient analysis. At each boosting round, the proposed method combines classifiers from all sites and creates a classifier ensemble on each site. The final classifier is constructed as an ensemble of all classifier ensembles built on disjoint data sets. The new proposed methods applied to several data sets have shown that parallel boosting can achieve the same or even better prediction accuracy considerably faster than the standard sequential boosting. Results from the experiments also indicate that distributed boosting has comparable or slightly improved classification accuracy over standard boosting, while requiring much less memory and computational time since it uses smaller data sets.

The Path Analysis Controversy: A New Statistical Approach to Strong Appraisal of Verisimilitude

Abstract: A new approach for using path analysis to appraise the verisimilitude of theories is described. Rather than trying to test a model's truth (correctness), this method corroborates a class of path diagrams by determining how well they predict intradata relations in comparison with other diagrams. The observed correlation matrix is partitioned into disjoint sets. One set is used to estimate the model parameters, and a nonoverlapping set is used to assess the model's verisimilitude. Computer code was written to generate competing models and to test the conjectured model's superiority (relative to the generated set) using diagram combinatorics and is available on the Web (http://www.vanderbilt.edu/quantmetheval/downloads.htm).

Advances in Polynomial Continuation for Solving Problems in Kinematics

Abstract: For many mechanical systems, including nearly all robotic manipulators, the set of possible configurations that the links may assume can be described by a system of polynomial equations. Thus, solving such systems is central to many problems in analyzing the motion of a mechanism or in designing a mechanism to achieve a desired motion. This paper describes techniques, based on polynomial continuation, for numerically solving such systems. Whereas in the past, these techniques were focused on finding isolated roots, we now address the treatment of systems having higher-dimensional solution sets. Special attention is given to cases of exceptional mechanisms, which have an higher degree of freedom of motion than predicted by their mobility. In fact, such mechanisms often have several disjoint assembly modes, and the degree of freedom of motion is not necessarily the same in each mode. Our algorithms identify all such assembly modes, determine their dimension and degree, and give sample points on each.Copyright © 2002 by ASME

Routing and wavelength assignment in optical networks from edge disjoint path algorithms

Abstract: Routing and wavelength assignment (RWA) problems in wavelength-routed optical networks are typically solved using a combination of integer programming and graph coloring. Such techniques are complex and make extensive use of heuristics. We explore an alternative solution technique in the well-known maximum edge disjoint paths (EDP) problem which can be naturally adapted to the RWA problem. Maximum EDP is NP-hard, but now it is known that simple greedy algorithms for it are as good as any of the more complex heuristic solutions. In this paper we investigate the performance of a simple greedy maximum edge disjoint paths algorithm applied to the RWA problem and compare it with a previously known solution method.

A Pseudo-Metric for Weighted Point Sets

Abstract: We derive a pseudo-metric for weighted point sets There are numerous situations, for example in the shape description domain, where the individual points in a feature point set have an associated attribute, a weight A distance function that incorporates this extra information apart from the points' position can be very useful for matching and retrieval purposes There are two main approaches to do this One approach is to interpret the point sets as fuzzy sets However, a distance measure for fuzzy sets that is a metric, invariant under rigid motion and respects scaling of the underlying ground distance, does not exist In addition, a Hausdorff-like pseudo-metric fails to differentiate between fuzzy sets with arbitrarily different maximum memebership values The other approach is the Earth Mover's Distance However, for sets of unequal total weights, it gives zero distance for arbitrarily different sets, and does not obey the triangle inequality In this paper we derive a distance measure, based on weight transportation, that is invariant under rigid motion, respects scaling, and obeys the triangle inequality, so that it can be used in efficient database searching Moreover, our pseudo-metric identifies only weight-scaled versions of the same set We demonstrate its potential use by testing it on two different collections, one of company logos and another one of fish contours

R = 0 spacetimes and self-dual Lorentzian wormholes

Abstract: A two-parameter family of spherically symmetric, static Lorentzian wormholes is obtained as the general solution of the equation $\ensuremath{\rho}={\ensuremath{\rho}}_{t}=0,$ where $\ensuremath{\rho}{=T}_{\mathrm{ij}}{u}^{i}{u}^{j},$ ${\ensuremath{\rho}}_{t}{=(T}_{\mathrm{ij}}\ensuremath{-}\frac{1}{2}{\mathrm{Tg}}_{\mathrm{ij}}{)u}^{i}{u}^{j},$ and ${u}^{i}{u}_{i}=\ensuremath{-}1.$ This equation characterizes a class of spacetimes which are ``self-dual'' (in the sense of electrogravity duality). The class includes the Schwarzschild black hole, a family of naked singularities, and a disjoint family of Lorentzian wormholes, all of which have a vanishing scalar curvature $(R=0).$ The properties of these spacetimes are discussed. Using isotropic coordinates we delineate clearly the domains of parameter space for which wormholes, nakedly singular spacetimes and the Schwarzschild black hole can be obtained. A model for the required ``exotic'' stress-energy is discussed, and the notion of traversability for the wormholes is also examined.

Polynomial-time approximation schemes for geometric min-sum median clustering

Abstract: The Johnson--Lindenstrauss lemma states that n points in a high-dimensional Hilbert space can be embedded with small distortion of the distances into an O(log n) dimensional space by applying a random linear transformation. We show that similar (though weaker) properties hold for certain random linear transformations over the Hamming cube. We use these transformations to solve NP-hard clustering problems in the cube as well as in geometric settings.More specifically, we address the following clustering problem. Given n points in a larger set (e.g., ℝd) endowed with a distance function (e.g., L2 distance), we would like to partition the data set into k disjoint clusters, each with a "cluster center," so as to minimize the sum over all data points of the distance between the point and the center of the cluster containing the point. The problem is provably NP-hard in some high-dimensional geometric settings, even for k = 2. We give polynomial-time approximation schemes for this problem in several settings, including the binary cube {0,1}d with Hamming distance, and ℝd either with L1 distance, or with L2 distance, or with the square of L2 distance. In all these settings, the best previous results were constant factor approximation guarantees.We note that our problem is similar in flavor to the k-median problem (and the related facility location problem), which has been considered in graph-theoretic and fixed dimensional geometric settings, where it becomes hard when k is part of the input. In contrast, we study the problem when k is fixed, but the dimension is part of the input.

Disjoint reference and the typology of pronouns

Abstract: Obviation versus Blocking. Two approachesto the distribution of anaphorsand pronominalshavebeenexploredin Binding Theory. TheOBVIATION approach,originating in Lasnik 1976 and extensivelydevelopedin the GB tradition, posits autonomousdisjoint referenceprincipleswhichdirectly filter out illicit coindexationsin certainstructuraldomains.TheBLOCKING approachtreatsdisjoint referencederivatively, by makinganaphorsobligatoryundercoreferencein thebinding domain,and invoking asyntacticor pragmaticprinciple thatforcesdisjoint referencepronominals in the“elsewhere”case. 1

Method and system for analysis of database records having fields with sets

Abstract: A method for analyzing a plurality of sets of elements (120, 140). Transaction analyzer (160) determines transactions (170) which sets from among the plurality of sets have elements in common with a trial set, including arranging a stored plurality of sets according to a directed graph data structure, the directed graph including nodes that correspond to sets and including directed edges that correspond to a relationship of set-wise inclusion, for a given trial set, denoted T, finding, within the directed graph, a smallest set, denoted S, that contains T, and determining whether T has a non-empty intersection with sets of the directed graph that are contained within S. A system is also described and claimed.

Bonding, moment formation, and magnetic interactions in Ca14MnBi11 and Ba14MnBi11

Abstract: ``14-1-11'' phase compounds, based on magnetic Mn ions and typified by ${\mathrm{Ca}}_{14}{\mathrm{MnBi}}_{11}$ and ${\mathrm{Ba}}_{14}{\mathrm{MnBi}}_{11},$ show an unusual magnetic behavior, but the large number (104) of atoms in the primitive cell has precluded any previous full electronic structure study. Using an efficient, local-orbital-based method within the local-spin-density approximation to study the electronic structure, we find a gap between a bonding valence-band complex and an antibonding conduction-band continuum. The bonding bands lack one electron per formula unit of being filled, making them low carrier density p-type metals. The hole resides in the ${\mathrm{MnBi}}_{4}$ tetrahedral unit, and partially compensates for the high-spin ${d}^{5} \mathrm{Mn}$ moment, leaving a net spin near $4{\ensuremath{\mu}}_{B}$ that is consistent with experiment. These manganites are composed of two disjoint but interpenetrating ``jungle gym'' networks of spin-$\frac{4}{2}$ ${\mathrm{MnBi}}_{4}^{9\ensuremath{-}}$ units with ferromagnetic interactions within the same network, and weaker couplings between the networks whose sign and magnitude is sensitive to materials parameters. ${\mathrm{Ca}}_{14}{\mathrm{MnBi}}_{11}$ is calculated to be ferromagnetic as observed, while for ${\mathrm{Ba}}_{14}{\mathrm{MnBi}}_{11}$ (which is antiferromagnetic) the ferromagnetic and antiferromagnetic states are calculated to be essentially degenerate. The band structure of the ferromagnetic states is very close to half metallic.

An inequality for laminations, Julia sets and `growing trees'

Abstract: For a closed lamination on the unit circle invariant under z\mapsto z^d we prove an inequality relating the number of points in the ‘gaps’ with infinite pairwise disjoint orbits to the degree; in particular, this gives estimates on the cardinality of any such ‘gap’ as well as on the number of distinct grand orbits of such ‘gaps’. As a tool, we introduce and study a dynamically defined growing tree in the quotient space. We also use our techniques to obtain for laminations an analog of Sullivan's no wandering domain theorem. Then we apply these results to Julia sets of polynomials.

An explicit scattering, non-weakly mixing example and weak disjointness

Abstract: By a dynamical system we mean a pair (X,T), where X is a compact metric space and T:X→X is surjective and continuous. We study weak disjointness in topological dynamics. (X,T) is scattering iff it is weakly disjoint from all minimal systems and (X,T) is strongly scattering iff it is weakly disjoint from all E-systems, i.e. transitive systems having invariant measures with full support. It is clear that a weakly mixing system is strongly scattering and the latter is scattering. An existential proof of scattering and a non-weakly mixing example is obtained by Akin and Glasner (2001 J. Anal. Math. 84 243-86). In this paper, we will give an explicit example which is strongly scattering and not weakly mixing. We also define extreme scattering, weak scattering and study the relationships of the various definitions. For a dynamical property P stronger than transitivity, let P be the property such that a system has P iff it is weakly disjoint from any system having P. We show that P = P. Moreover, we prove that (thickly syndetic-transitive) = piecewise-syndetic-transitive and (piecewise-syndetic-transitive) = thickly syndetic-transitive.

On a hypergraph Turan problem of Frankl

Abstract: Let $C^{2k}_r$ be the $2k$-uniform hypergraph obtained by letting $P_1,...,P_r$ be pairwise disjoint sets of size $k$ and taking as edges all sets $P_i \cup P_j$ with $i eq j$. This can be thought of as the `$k$-expansion' of the complete graph $K_r$: each vertex has been replaced with a set of size $k$. We determine the exact Turan number of $C^{2k}_3$ and the corresponding extremal hypergraph, thus confirming a conjecture of Frankl. Sidorenko has given an upper bound of $(r-2) / (r-1)$ for the Tur\'an density of $C^{2k}_r$ for any $r$, and a construction establishing a matching lower bound when $r$ is of the form $2^p + 1$. We show that when $r = 2^p + 1$, any $C^4_r$-free hypergraph of density $(r-2)/(r-1) - o(1)$ looks approximately like Sidorenko's construction. On the other hand, when $r$ is not of this form, we show that corresponding constructions do not exist and improve the upper bound on the Tur\'an density of $C^4_r$ to $(r-2)/(r-1) - c(r)$, where $c(r)$ is a constant depending only on $r$. The backbone of our arguments is a strategy of first proving approximate structure theorems, and then showing that any imperfections in the structure must lead to a suboptimal configuration. The tools for its realisation draw on extremal graph theory, linear algebra, the Kruskal-Katona theorem and properties of Krawtchouck polynomials.

Shell partition and metric semispaces: Minkowski norms, root scalar products, distances and cosines of arbitrary order

Abstract: Vector semispaces are studied from a realistic way with the intention to define a natural metric, adapted to their peculiar structure, which reside on the essential positive definiteness of their elements From this point of view, Minkowski norms allow classifying semispaces in shells, that is: subsets where all the vector elements possess the same norm values Shell structure appears to be a possible disjoint partition of any semispace and so shells become equivalence classes Then, the unit shell appears to be the core of the semispace homothetic construction as well as the origin of the semispace metrics Minkowski or root scalar products permit to connect two or more semispace elements and conduct towards generalized definitions of Pth order root distances and cosines Finally, the unit shell of a given semispace, in company of both Boolean tagged sets, inward matrix products and with the aid of the matrix signatures as well, it is seen as the seed to construct any arbitrary element of the semispace connected vector space Finite and infinite dimensional vector spaces application examples are provided along the work discussion

Constructing one-to-many disjoint paths in folded hypercubes

Abstract: Routing functions have been shown effective in deriving disjoint paths in the hypercube. In this paper, using a minimal routing function, k+1 disjoint paths from one node to another k+1 distinct nodes are constructed in a k-dimensional folded hypercube whose maximal length is not greater than the diameter plus one, which is minimum in the worst case. For the general case, the maximal length is nearly optimal (/spl les/ the maximal distance between the two end nodes of these k+1 paths plus two). As a by-product, the Rabin number of the folded hypercube is obtained, which is an open problem raised by S.C. Liaw and G.J. Chang (1999).

Sorting and searching using ternary CAMs

Abstract: Sorting and searching are classic problems in computing and several RAM based solutions exist. We present sorting and searching algorithms using TCAMs. Using these algorithms, one can perform sorting in O(n) memory cycles using a TCAM. Furthermore, inserts and deletes to a sorted list and priority queue operations can be done in O(1) cycles. A searching problem may typically involve finding if a query point is contained in a given set of ranges. We call this the point intersection problem. The ranges may be inserted or deleted from the set dynamically. For these problems, we present several algorithms with different time, space and implementation complexity tradeoffs. One of the algorithms uses only O(1) time for all operations and O(1) space for each range in the set when the ranges are disjoint. More precisely, one can perform disjoint range search in one memory cycle using a 2-stage pipeline. We also provide several solutions in scenarios where the ranges in the set are allowed to overlap.

An efficient multi-variable inversion algorithm for reliability evaluation of complex systems using path sets

Abstract: Reliability evaluation of a large and complex system is quite an involved and time-consuming process and its state-of-art is far from being called as satisfactory. This is mainly due to the fact that unionizing path sets results in large number of terms in the reliability expression. Thereafter, the process of computing numerical value of system reliability from its expression is a task not free from the build up of round-off errors. The entire process also restricts the use of a low-end PC for computing system reliability of such systems. In this paper, we propose an efficient methodology to evaluate reliability of large and complex systems based on minimal path sets; the path sets enumeration procedure used in this paper generates path sets in lexicographic and increasing order of cardinality — a condition, which is helpful in obtaining sum of disjoint products (SDP) of the system reliability expression in a compact form. Although we make use of the system connection matrix but no complicated matrix operations are performed to obtain the results. The paper further presents an improved multi-variable inversion (MVI) algorithm to evaluate system reliability in a compact form. Our approach offers an extensive reduction in the number of mutually disjoint terms and provides a minimized and compact system reliability expression. The procedure not only results in substantial saving of CPU time but also can be run on a low-end PC. To demonstrate this capability, we solve several problems of varied complexities on a low-end PC and also provide a comparison of our approach with earlier techniques available for the purpose.

Robust Matchings

Abstract: We consider complete graphs with nonnegative edge weights. A p-matching is a set of p disjoint edges. We prove the existence of a maximal (with respect to inclusion) matching M that contains for any $p\le|M|$ $p$ edges whose total weight is at least ${1\over \sqrt 2}$ of the maximum weight of a p-matching. We use this property to approximate the metric maximum clustering problem with given cluster sizes.

Kinetic maintenance of context-sensitive hierarchical representations for disjoint simple polygons

Abstract: We describe how to construct and kinetically maintain a tessellation of the free space between a collection of k disjoint simple polygonal objects with a total of N vertices, R of which are reflex. Our linear size tessellation consists of pseudo-triangles and has the following properties: (i) it contains disjoint outer hierarchical representations of all objects where the size of the outer boundary of these representations is proportional to a minimum link separator for the objects, and (ii) any line segment in the free space intersects at most O((k + log R) log N) pseudo-triangles (each of constant size).We maintain our tessellation by using the Kinetic Data Structure (KDS) framework. Our structure is compact, maintaining an active set of certificates whose number is linear in the size of a minimum link subdivision for the objects. It is also responsive; on the failure of a certificate invariants can be restored in time logarithmic in the total number of vertices. While its efficiency is difficult to establish precisely, it is shown that at most O(k + κmaxlog R)log N events happen during straight line motion of one object A in the context of k (fixed) others, where κmax denotes the maximum size of the minimum link polygon separating object A from the rest, during the motion.Furthermore, ray shooting queries (that use point location) can be answered in O((k + log R) log N) time for rays with arbitrary direction.

On the Geometry of Orientation-Preserving Planar Piecewise Isometries

Abstract: {Planar piecewise isometries (PWIs) are iterated mappings of subsets of the plane that preserve length (and hence angle and area) on each of a number of disjoint regions. They arise naturally in several applications and are a natural generalization of the well-studied interval exchange transformations. {The aim of this paper is to propose and investigate basic properties of orientation-preserving PWIs. We develop a framework with which one can classify PWIs of a polygonal region of the plane with polygonal partition. Basic dynamical properties of such maps are discussed and a number of results are proved that relate dynamical properties of the maps to the geometry of the partition. It is shown that the set of such mappings on a given number of polygons splits into a finite number of families; we call these classes. These classes may be of varying dimension and may or may not be connected. } {The classification of PWIs on n triangles for n up to 3 is discussed in some detail, and several specific cases where n is larger than three are examined. To perform this classification, equivalence under similarity is considered, and an associated perturbation dimension is defined as the dimension of a class of maps modulo this equivalence. A class of PWIs is said to be rigid if this perturbation dimension is zero.} A variety of rigid and nonrigid classes and several of these rigid classes of PWI s are found. In particular, those with angles that are multiples of π/n for n=3 , 4 , and 5 give rise to self-similar structures in their dynamical refinements that are considerably simpler than those observed for other angles.}