The topographic information of a closed world is expressed as a graph. The plural mov- ingobjects which go and back in it according to a single moving strategy are supposed.The moving strategy is expressed by numerica...The topographic information of a closed world is expressed as a graph. The plural mov- ingobjects which go and back in it according to a single moving strategy are supposed.The moving strategy is expressed by numerical values as a decision table. Coding is performed with this table as chromosomes, and this is optimized by using genetic algorithm. These environments were realized on a computer, and the simulation was carried out. As the result, the learning of the method to act so that moving objects do not obstruct mutually was recognized, and it was confirmed that these methods are effective for optimizing moving strategy.展开更多
We analyze a common feature of p-Kemeny AGGregation（p-KAGG） and p-One-Sided Crossing Minimization（p-OSCM） to provide new insights and findings of interest to both the graph drawing community and the social choice ...We analyze a common feature of p-Kemeny AGGregation（p-KAGG） and p-One-Sided Crossing Minimization（p-OSCM） to provide new insights and findings of interest to both the graph drawing community and the social choice community. We obtain parameterized subexponential-time algorithms for p-KAGG—a problem in social choice theory—and for p-OSCM—a problem in graph drawing. These algorithms run in time O＊（2O（√k log k））,where k is the parameter, and significantly improve the previous best algorithms with running times O.1.403k/and O.1.4656k/, respectively. We also study natural ＂above-guarantee＂ versions of these problems and show them to be fixed parameter tractable. In fact, we show that the above-guarantee versions of these problems are equivalent to a weighted variant of p-directed feedback arc set. Our results for the above-guarantee version of p-KAGG reveal an interesting contrast. We show that when the number of ＂votes＂ in the input to p-KAGG is odd the above guarantee version can still be solved in time O＊（2O（√k log k））, while if it is even then the problem cannot have a subexponential time algorithm unless the exponential time hypothesis fails（equivalently, unless FPT D M[1]）.展开更多
Algorithms used in data mining and bioinformatics have to deal with huge amount of data efficiently. In many applications, the data are supposed to have explicit or implicit structures. To develop efficient algorithms...Algorithms used in data mining and bioinformatics have to deal with huge amount of data efficiently. In many applications, the data are supposed to have explicit or implicit structures. To develop efficient algorithms for such data, we have to propose possible structure models and test if the models are feasible. Hence, it is important to make a compact model for structured data, and enumerate all instances efficiently. There are few graph classes besides trees that can be used for a model. In this paper, we investigate distance-hereditary graphs. This class of graphs consists of isometric graphs and hence contains trees and cographs. First, a canonical and compact tree representation of the class is proposed. The tree representation can be constructed in linear time by using prefix trees. Usually, prefix trees are used to maintain a set of strings. In our algorithm, the prefix trees are used to maintain the neighborhood of vertices, which is a new approach unlike the lexicographically breadth-first search used in other studies. Based on the canonical tree representation, efficient algorithms for the distance-hereditary graphs are proposed, including linear time algorithms for graph recognition and graph isomorphism and an efficient enumeration algorithm. An efficient coding for the tree representation is also presented; it requires [3.59n] bits for a distance-hereditary graph of n vertices and 3n bits for a cograph. The results of coding improve previously known upper bounds （both are 2^O（nlogn）） of the number of distance-hereditary graphs and cographs to 2^[3.59n] and 2^3n, respectively.展开更多
文摘The topographic information of a closed world is expressed as a graph. The plural mov- ingobjects which go and back in it according to a single moving strategy are supposed.The moving strategy is expressed by numerical values as a decision table. Coding is performed with this table as chromosomes, and this is optimized by using genetic algorithm. These environments were realized on a computer, and the simulation was carried out. As the result, the learning of the method to act so that moving objects do not obstruct mutually was recognized, and it was confirmed that these methods are effective for optimizing moving strategy.
基金supported by a GermanNorwegian PPP grantsupported by the Indo-German Max Planck Center for Computer Science (IMPECS)
文摘We analyze a common feature of p-Kemeny AGGregation（p-KAGG） and p-One-Sided Crossing Minimization（p-OSCM） to provide new insights and findings of interest to both the graph drawing community and the social choice community. We obtain parameterized subexponential-time algorithms for p-KAGG—a problem in social choice theory—and for p-OSCM—a problem in graph drawing. These algorithms run in time O＊（2O（√k log k））,where k is the parameter, and significantly improve the previous best algorithms with running times O.1.403k/and O.1.4656k/, respectively. We also study natural ＂above-guarantee＂ versions of these problems and show them to be fixed parameter tractable. In fact, we show that the above-guarantee versions of these problems are equivalent to a weighted variant of p-directed feedback arc set. Our results for the above-guarantee version of p-KAGG reveal an interesting contrast. We show that when the number of ＂votes＂ in the input to p-KAGG is odd the above guarantee version can still be solved in time O＊（2O（√k log k））, while if it is even then the problem cannot have a subexponential time algorithm unless the exponential time hypothesis fails（equivalently, unless FPT D M[1]）.
基金presented at the 4th Annual Conference on Theory and Applications of Models of Computation(TAMC07)
文摘Algorithms used in data mining and bioinformatics have to deal with huge amount of data efficiently. In many applications, the data are supposed to have explicit or implicit structures. To develop efficient algorithms for such data, we have to propose possible structure models and test if the models are feasible. Hence, it is important to make a compact model for structured data, and enumerate all instances efficiently. There are few graph classes besides trees that can be used for a model. In this paper, we investigate distance-hereditary graphs. This class of graphs consists of isometric graphs and hence contains trees and cographs. First, a canonical and compact tree representation of the class is proposed. The tree representation can be constructed in linear time by using prefix trees. Usually, prefix trees are used to maintain a set of strings. In our algorithm, the prefix trees are used to maintain the neighborhood of vertices, which is a new approach unlike the lexicographically breadth-first search used in other studies. Based on the canonical tree representation, efficient algorithms for the distance-hereditary graphs are proposed, including linear time algorithms for graph recognition and graph isomorphism and an efficient enumeration algorithm. An efficient coding for the tree representation is also presented; it requires [3.59n] bits for a distance-hereditary graph of n vertices and 3n bits for a cograph. The results of coding improve previously known upper bounds （both are 2^O（nlogn）） of the number of distance-hereditary graphs and cographs to 2^[3.59n] and 2^3n, respectively.
