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Improving Discrete Mathematics and Algorithms Curricula with LINK
, 1997
"... This paper introduces the LINK system as an educational tool which can be used to visualize and experiment with discrete algorithms. An extended example demonstrates the flexibility of the system in the context of a fundamental graph algorithm: finding the strongly connected components of a directed ..."
Abstract

Cited by 9 (2 self)
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This paper introduces the LINK system as an educational tool which can be used to visualize and experiment with discrete algorithms. An extended example demonstrates the flexibility of the system in the context of a fundamental graph algorithm: finding the strongly connected components of a directed graph.
LINK: A Combinatorics and Graph Theory Workbench for Applications and Research
, 1995
"... LINK is a set of C++ class libraries that supports applications in discrete mathematics. The libraries include a commandline interpreter and a graphical user interface that allow access to basic data structures such as Sets and Lists, and a graph hierarchy that includes undirected, directed, and &qu ..."
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Cited by 2 (1 self)
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LINK is a set of C++ class libraries that supports applications in discrete mathematics. The libraries include a commandline interpreter and a graphical user interface that allow access to basic data structures such as Sets and Lists, and a graph hierarchy that includes undirected, directed, and "mixed" hypergraphs and graphs. A "mixed" graph may contain both directed and undirected edges. Many standard data structures including arrays, lists, heaps and binary search trees are within a Container hierarchy. Sets and Sequences are supported within a Collection hierarchy. The data structure hierarchies enable the user to experiment with competing data structure implementations, and with more complex and sophisticated data structures. If an algorithm has several possible choices of a data structure to be used, a single object can be created that is templated with the particular data structure desired. LINK also contains a set of graph generators, layout algorithms for hypergraphs and binar...
Computers and Discovery in Algebraic Graph Theory
 Edinburgh, 2001), Linear Algebra Appl
, 2001
"... We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory. ..."
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Cited by 1 (0 self)
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We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.
Implementing Progress Indicators For Recursive Algorithms
"... A percentdone progress indicator is a software tool that allows a user to monitor the progress that a software system has made toward responding to a command. Formal experiments have demonstrated that users prefer software systems that incorporate percentdone progress indicators over those that do ..."
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Cited by 1 (0 self)
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A percentdone progress indicator is a software tool that allows a user to monitor the progress that a software system has made toward responding to a command. Formal experiments have demonstrated that users prefer software systems that incorporate percentdone progress indicators over those that do not. Obviously, a system must be able to calculate (or at least estimate) the percentage of a computation that has been completed in order to support a percentdone progress indicator. This is generally straightforward for programs that make a fixed number of linear passes over their input and then terminate (e.g., file transfer programs). Most previous percentdone progress indicators have been limited to such programs. This paper presents a new technique called "dynamic bound evaluation" that allows percentdone progress indicators to be routinely incorporated into a wide range of programs that are driven by recursive algorithms that are not required to follow the "linear pass over data" p...
LINK: Exploring Combinatorial Objects
, 1996
"... This paper introduces the Link system for exploring combinatorial objects. It provides graphical and functional language interfaces which are user friendly and flexible, and includes a detachable set of C++ libraries. Link allows us to interactively explore the structure of combinatorial objects suc ..."
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This paper introduces the Link system for exploring combinatorial objects. It provides graphical and functional language interfaces which are user friendly and flexible, and includes a detachable set of C++ libraries. Link allows us to interactively explore the structure of combinatorial objects such as collections, graphs, and hypergraphs. Graphs and Hypergraphs can be defined in which multiple edges are allowed or not, and in which edge sets can contain undirected edges, directed edges, or both types. Full support for default and userdefined attributes is included. We examine the use of Link in the context of a clustering problem which is a natural application for the use of hypergraphs. Realworld problems calling for the manipulation of hypergraphs or heavily attributed graphs are often simplified to avoid overcomplicated implementations. Link allows the user to define, manipulate, and visualize such combinatorial objects at a very high level. 1 Introduction For many years many d...
Monitoring an Algorithm's Execution
"... . Many software systems for Discrete Mathematics incorporate routines that compute NPhard functions. In spite of their worstcase exponential running time, there are often a wide range of inputs for which these routines run in interactive time. It is generally dicult for a user to distinguish, a ..."
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. Many software systems for Discrete Mathematics incorporate routines that compute NPhard functions. In spite of their worstcase exponential running time, there are often a wide range of inputs for which these routines run in interactive time. It is generally dicult for a user to distinguish, a priori, the \easy" inputs from those that are \hard". A percentdone progress indicator is a software tool that allows a user to monitor the percentage of a computation that has been completed. Such indicators have been implemented for linear algorithms (e.g., le transfer programs). This paper introduces a paradigm which we call dynamic bound evaluation for monitoring the progress of a wide class of recursive algorithms that need not be linear. Further, empirical results are presented that illustrate the eectiveness of the technique as it has been implemented in the SetPlayer system for symbolic set manipulation. 1. Introduction and motivation Many software systems incorporate a...
LINK: A Software System for Experimentation with Graphs and
, 1997
"... In the recent past, there have been several efforts to construct software systems for discrete mathematics, and in particular, for the manipulation of graphs. None, however, has resulted in a product with influence comparable to the nowfamiliar symbolic mathematics packages. ..."
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In the recent past, there have been several efforts to construct software systems for discrete mathematics, and in particular, for the manipulation of graphs. None, however, has resulted in a product with influence comparable to the nowfamiliar symbolic mathematics packages.
An Informal Preview of the Link System
, 1996
"... This document gives a preview of Link, a software system for graph theory and combinatorics which will be useful in both research and education. It should be ..."
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This document gives a preview of Link, a software system for graph theory and combinatorics which will be useful in both research and education. It should be