7083057
LexBFS-Ordering in Asteroidal Triple-Free Graphs
In this paper, we study the metric property of LexBFS-ordering on AT-free graphs. Based on a 2-sweep LexBFS algorithm, we show that every AT-free graph admits a vertex ordering, called the strong 2-cocomparability ordering, that for any three vertices u ≺ v ≺ w in the ordering, if d(u, w) ≤ 2 then d(u, v) = 1 or d(v, w) ≤ 2. As an application of this ordering, we provide a simple linear time recognition algorithm for bipartite permutation graphs, which form a subclass of AT-free graphs.
44408883
Hamiltonian-laceability of star graphs
12861854
The Recognition of Geodetically Connected Graphs
Abstract Let G = ( V , E ) be a graph with vertex set V of size n and edge set E of size m . A vertex υ ϵ V is called a hinge vertex if the distance of any two vertices becomes longer after v is removed. A graph without hinge vertex is called a hinge-free graph. In general, a graph G is k -geodetically connected or k -GC for short if G can tolerate any k − 1 vertices failures without increasing the distance among all the remaining vertices. In this paper, we show that recognizing a graph G to be k -GC for the largest value of k can be solved in O ( nm ) time. In addition, more efficient algorithms for recognizing the k -GC property on some special graphs are presented. These include the O ( n + m ) time algorithms on strongly chordal graphs (if a strong elimination ordering is given), ptolemaic graphs, and interval graphs, and an O ( n 2 ) time algorithm on undirected path graphs (if a characteristic tree model is given). Moreover, we show that if the input graph G is not hinge-free then finding all hinge vertices of G can be solved in the same time complexity on the above classes of graphs.
10538824
Parallel Decomposition of Generalized Series-Parallel Graphs
Generalized series-parallel (GSP) graphs belong to the class of decomposable graphs which can be represented by their decomposition trees. Given a decomposition tree of a GSP graph, there are many graph-theoretic problems which can be solved efficiently. An efficient parallel algorithm for constructing a decomposition tree of a given GSP graph is presented. It takes O(log n) time with C(m, n) processors on a CRCW PRAM, where C(m, n) is the number of processors required to find connected components of a graph with in edges and n vertices in logarithmic time. Based on our algorithmic results, we also derive some properties for GSP graphs, which may be of interest in and of themselves.
29920941
Counting Clique Trees and Computing Perfect Elimination Schemes in Parallel
Abstract In a previous result, the authors showed that a clique tree of a chordal graph can be constructed in O(log n ) parallel computing time with O( n 3 ) processors on CRCW PRAM, where n is the number of nodes of the graph. In this paper, it will be shown that this result can be extended in two ways. First, we show that from the parallel clique tree constructing algorithm, we can derive an exact formula of counting clique trees of a labeled connected chordal graph. Next, we show that a perfect elimination scheme of a chordal graph can be computed in O(log n ) time with O( n 2 ) processors on CREW PRAM once a clique tree of the graph is given. This implies that a perfect elimination scheme of a chordal graph can be computed in O(log n ) time with O( n 3 ) processors on CRCW PRAM.
1980858
Edge and Node Searching Problems on Trees
In this paper, we show that there is a natural correspondence between a tree's edge-search strategy and its node-search strategy. By doing so, we simplify the previous linear time algorithm for determining the edge-search number of a tree, and improve the running time of a previous algorithm for constructing an edge-search strategy (or plan) for a tree containing n vertices from O(n log n) to O(n) time.
13524203
Haptic discrimination of force direction and the influence of visual information
Despite a wealth of literature on discrimination thresholds for displacement, force magnitude, stiffness, and viscosity, there is currently a lack of data on our ability to discriminate force directions. Such data are needed in designing haptic rendering algorithms where force direction, as well as force magnitude, are used to encode information such as surface topography. Given that haptic information is typically presented in addition to visual information in a data perceptualization system, it is also important to investigate the extent to which the congruency of visual information affects force-direction discrimination. In this article, the authors report an experiment on the discrimination threshold of force directions under the three display conditions of haptics alone (H), haptics plus congruent vision (HVcong), and haptics plus incongruent vision (HVincong). Average force-direction discrimination thresholds were found to be 18.4°, 25.6°, and 31.9° for the HVcong, H and HVincong conditions, respectively. The results show that the congruency of visual information significantly affected haptic discrimination of force directions, and that the force-direction discrimination thresholds did not seem to depend on the reference force direction. The implications of the results for designing haptic virtual environments, especially when the numbers of sensors and actuators in a haptic display do not match, are discussed.
8958554
Nested mappings: schema mapping reloaded
Many problems in information integration rely on specifications, called schema mappings, that model the relationships between schemas. Schema mappings for both relational and nested data are well-known. In this work, we present a new formalism for schema mapping that extends these existing formalisms in two significant ways. First, our nested mappings allow for nesting and correlation of mappings. This results in a natural programming paradigm that often yields more accurate specifications. In particular, we show that nested mappings can naturally preserve correlations among data that existing mapping formalisms cannot. We also show that using nested mappings for purposes of exchanging data from a source to a target will result in less redundancy in the target data. The second extension to the mapping formalism is the ability to express, in a declarative way, grouping and data merging semantics. This semantics can be easily changed and customized to the integration task at hand. We present a new algorithm for the automatic generation of nested mappings from schema matchings (that is, simple element-to-element correspondences between schemas). We have implemented this algorithm, along with algorithms for the generation of transformation queries (e.g., XQuery) based on the nested mapping specification. We show that the generation algorithms scale well to large, highly nested schemas. We also show that using nested mappings in data exchange can drastically reduce the execution cost of producing a target instance, particularly over large data sources, and can also dramatically improve the quality of the generated data.
641485
Mapping XML and relational schemas with Clio
Merging and coalescing data from multiple and diverse sources into different data formats continues to be an important problem in modern information systems. Schema matching (the process of matching elements of a source schema with elements of a target schema) and schema mapping (the process of creating a query that maps between two disparate schemas) are at the heart of data integration systems. We demonstrate Clio, a semi-automatic schema mapping tool developed at the IBM Almaden Research Center. In this paper, we showcase Clio's mapping engine which allows mapping to and from relational and XML schemas, and takes advantage of data constraints in order to preserve data associations.
1145137
Agent-assisted collaborative concept map
Merlin is a collaborative concept map that enables students to discuss their ideas. The agent in Merlin aims to monitor the students' content of discussion in order to provide context-sensitive help. Keywords in the students' discussion in a chat box are compared to the knowledge domain and appropriate support material is adapted to the student model. Instructional media is generated using design patterns.
44418101
Degree-constrained minimum spanning tree
Abstract In this paper the problem of a degree-constrained minimum spanning tree (DCMST) is defined. The problem is formulated as a linear 0–1 integer programming problem. A primal and a dual heuristic (construction) procedure and a branch-and-bound algorithm are proposed to construct a DCMST. These procedures are illustrated with a simple example. Some computational experience with these algorithms is also reported.