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46
Complexity and Algorithms for Reasoning About Time: A GraphTheoretic Approach
, 1992
"... Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified. This work unifies notions of interval algebras in artificial intelligence ..."
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Cited by 86 (11 self)
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Temporal events are regarded here as intervals on a time line. This paper deals with problems in reasoning about such intervals when the precise topological relationship between them is unknown or only partially specified. This work unifies notions of interval algebras in artificial intelligence with those of interval orders and interval graphs in combinatorics. The satisfiability, minimal labeling, all solutions and all realizations problems are considered for temporal (interval) data. Several versions are investigated by restricting the possible interval relationships yielding different complexity results. We show that even when the temporal data comprises of subsets of relations based on intersection and precedence only, the satisfiability question is NPcomplete. On the positive side, we give efficient algorithms for several restrictions of the problem. In the process, the interval graph sandwich problem is introduced, and is shown to be NPcomplete. This problem is als...
Graph Sandwich Problems
, 1994
"... The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly o ..."
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Cited by 49 (8 self)
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The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly on properties characterizing subfamilies of perfect graphs, we give polynomial algorithms for several properties and prove the NPcompleteness of others. We describe
Pathwidth, Bandwidth and Completion Problems to Proper Interval Graphs with Small Cliques
 SIAM Journal on Computing
, 1996
"... We study two related problems motivated by molecular biology: ffl Given a graph G and a constant k, does there exist a supergraph G of G which is a unit interval graph and has clique size at most k? ffl Given a graph G and a proper kcoloring c of G, does there exist a supergraph We show th ..."
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Cited by 29 (6 self)
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We study two related problems motivated by molecular biology: ffl Given a graph G and a constant k, does there exist a supergraph G of G which is a unit interval graph and has clique size at most k? ffl Given a graph G and a proper kcoloring c of G, does there exist a supergraph We show that those problems are polynomial for fixed k. On the other hand we prove that the first problem is equivalent to deciding if the bandwidth of G is at most k \Gamma 1. Hence, it is NPhard, and W [t]hard for all t. We also show that the second problem is W [1]hard. This implies that for fixed k, both of the problems are unlikely to have an O(n ) algorithm, where ff is a constant independent of k.
A Theory Of Classifier Combination: The Neural Network Approach
, 1995
"... There is a trend in recent OCR development to improve system performance by combining recognition results of several complementary algorithms. This thesis examines the classifier combination problem under strict separation of the classifier and combinator design. None other than the fact that every ..."
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Cited by 18 (0 self)
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There is a trend in recent OCR development to improve system performance by combining recognition results of several complementary algorithms. This thesis examines the classifier combination problem under strict separation of the classifier and combinator design. None other than the fact that every classifier has the same input and output specification is assumed about the training, design or implementation of the classifiers. A general theory of combination should possess the following properties. It must be able to combine anytype of classifiers regardless of the level of information contents in the outputs. In addition, a general combinator must be able to combine any mixture of classifier types and utilize all information available. Since classifier independence is difficult to achieve and to detect, it is essential for a combinator to handle correlated classifiers robustly. Although the performance of a robust (against correlation) combinator can be improved by adding classifiers indiscriminantly, it is generally of interest to achieve comparable performance with the minimum number of classifiers. Therefore, the combinator should have the ability to eliminate redundant classifiers. Furthermore, it is desirable to have a complexity control mechanism for the combinator. In the past, simplifications come from assumptions and constraints imposed by the system designers. In the general theory, there should be a mechanism to reduce solution complexity by exercising nonclassifierspecific constraints. Finally, a combinator should capture classifier/image dependencies. Nearly all combination methods have ignored the fact that classifier performances (and outputs) depend on various image characteristics, and this dependency is manifested in classifier output patterns in relation to input imag...
Maximizing Reward in a NonStationary Mobile Robot Environment
 Autonomous Agents and MultiAgent Systems
, 2002
"... The ability of a robot to improve its performance on a task can be critical, especially in poorly known and nonstationary environments where the best action or strategy is dependent upon the current state of the environment. In such systems, a good estimate of the current state of the environment i ..."
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Cited by 16 (0 self)
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The ability of a robot to improve its performance on a task can be critical, especially in poorly known and nonstationary environments where the best action or strategy is dependent upon the current state of the environment. In such systems, a good estimate of the current state of the environment is key to establishing high performance, however quantified. In this paper, we present an approach to state estimation in poorly known and nonstationary mobile robot environments, focusing on its application to a mine collection scenario where performance is quantified using reward maximization. The approach is based on the use of augmented Markov models (AMMs), a subclass of semiMarkov processes. We have developed an algorithm for incrementally constructing arbitraryorder AMMs online. It is used to capture the interaction dynamics between a robot and its environment in terms of behavior sequences executed during the performance of a task. For the purposes of reward maximization in a nonstationary environment, multiple AMMs monitor events at different timescales and provide statistics used to select the AMM likely to have a good estimate of the environmental state. AMMs with redundant or outdated information are discarded, while attempting to maintain sucient data to reduce conformation to noise. This approach has been successfully implemented on a mobile robot performing a mine collection task. In the context of this task, we first present experimental results validating our reward maximization performance criterion. We then incorporate our algorithm for state estimation using multiple AMMs, allowing the robot to select appropriate actions based on the estimated state of the environment. The approach is tested first with a physical robot, in a nonstationary environment...
Combination of Structural Classifiers
, 1990
"... this paper, we demonstrate that this is possible, and propose a method that can be used to combine the decisions of individual classifiers to obtain a classification procedure which performs better than any of the individual classifiers ..."
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Cited by 14 (9 self)
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this paper, we demonstrate that this is possible, and propose a method that can be used to combine the decisions of individual classifiers to obtain a classification procedure which performs better than any of the individual classifiers
Learning Multiple Models for Reward Maximization
 In Seventeenth International Conference on Machine Learning
, 2000
"... We present an approach to reward maximization in a nonstationary mobile robot environment. The approach works within the realistic constraints of limited local sensing and limited a priori knowledge of the environment. It is based on the use of augmented Markov models (AMMs), a general modeli ..."
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Cited by 13 (5 self)
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We present an approach to reward maximization in a nonstationary mobile robot environment. The approach works within the realistic constraints of limited local sensing and limited a priori knowledge of the environment. It is based on the use of augmented Markov models (AMMs), a general modeling tool we have developed. AMMs are essentially Markov chains having additional statistics associated with states and state transitions. We have developed an algorithm that constructs AMMs online and in realtime with little computational and space overhead, making it practical to learn multiple models of the interaction dynamics between a robot and its environment during the execution of a task. For the purposes of reward maximization in a nonstationary environment, these models monitor events at increasing intervals of time and provide statistics used to discard redundant or outdated information while reducing the probability of conforming to noise. We have successfully i...
Applications and Variations of Domination in Graphs
, 2000
"... In a graph G =(V,E), S ⊆ V is a dominating set of G if every vertex is either in S or joined by an edge to some vertex in S. Many different types of domination have been researched extensively. This dissertation explores some new variations and applications of dominating sets. We first introduce the ..."
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Cited by 12 (0 self)
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In a graph G =(V,E), S ⊆ V is a dominating set of G if every vertex is either in S or joined by an edge to some vertex in S. Many different types of domination have been researched extensively. This dissertation explores some new variations and applications of dominating sets. We first introduce the concept of Roman domination. A Roman dominating function is a function f: V →{0, 1, 2} such that every vertex v for which f(v) =0hasa neighbor w with f(w) = 2. This corresponds to a problem in army placement where every region is either defended by its own army or has a neighbor with two armies, in which case one of the two armies can be sent to the undefended region if a conflict breaks out. The weight of a Roman dominating function f is f(V) = � v∈V f(v), and we are interested in finding Roman dominating functions of minimum weight. We explore the graph theoretic, algorithmic, and complexity issues of Roman domination, including algorithms for finding minimum weight Roman dominating functions for trees and grids.
Dynamic systems as tools for analysing human judgement
 THINKING AND RESONING
, 2001
"... With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review of this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approach ..."
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Cited by 11 (8 self)
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With the advent of computers in the experimental labs, dynamic systems have become a new tool for research on problem solving and decision making. A short review of this research is given and the main features of these systems (connectivity and dynamics) are illustrated. To allow systematic approaches to the influential variables in this area, two formal frameworks (linear structural equations and finite state automata) are presented. Besides the formal background, the article sets out how the task demands of system identification and system control can be realised in these environments, and how psychometrically acceptable dependent variables can be derived. The use of computersimulated scenarios in problemsolving research has become increasingly popular during the last 25 years (for a representative collection of papers see, e.g., the two editions from Sternberg & Frensch, 1991, and Frensch & Funke, 1995). This new approach to problem solving seems attractive for several reasons. In contrast to static problems, computersimulated scenarios provide a unique opportunity to study human problemsolving and decisionmaking behaviour when the task environment and subjects ’ actions change concurrently. Subjects can manipulate a specific scenario via a number of input variables (typically ranging from 2 to 20, and in some exceptional instances even up to 2000), and they observe the system’s state changes in a number of output variables. In exploring and/or controlling a system, subjects have to continuously acquire and use knowledge about the internal structure of the system.
New perspectives on interval orders and interval graphs
 in Surveys in Combinatorics
, 1997
"... Abstract. Interval orders and interval graphs are particularly natural examples of two widely studied classes of discrete structures: partially ordered sets and undirected graphs. So it is not surprising that researchers in such diverse fields as mathematics, computer science, engineering and the so ..."
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Cited by 7 (5 self)
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Abstract. Interval orders and interval graphs are particularly natural examples of two widely studied classes of discrete structures: partially ordered sets and undirected graphs. So it is not surprising that researchers in such diverse fields as mathematics, computer science, engineering and the social sciences have investigated structural, algorithmic, enumerative, combinatorial, extremal and even experimental problems associated with them. In this article, we survey recent work on interval orders and interval graphs, including research on online coloring, dimension estimates, fractional parameters, balancing pairs, hamiltonian paths, ramsey theory, extremal problems and tolerance orders. We provide an outline of the arguments for many of these results, especially those which seem to have a wide range of potential applications. Also, we provide short proofs of some of the more classical results on interval orders and interval graphs. Our goal is to provide fresh insights into the current status of research in this area while suggesting new perspectives and directions for the future. 1.