It is desired to obtain the joint probability distribution(JPD) over a set of random variables with local data, so as to avoid the hard work to collect statistical data in the scale of all variables. A lot of work has...It is desired to obtain the joint probability distribution(JPD) over a set of random variables with local data, so as to avoid the hard work to collect statistical data in the scale of all variables. A lot of work has been done when all variables are in a known directed acyclic graph(DAG). However, steady directed cyclic graphs(DCGs) may be involved when we simply combine modules containing local data together, where a module is composed of a child variable and its parent variables. So far, the physical and statistical meaning of steady DCGs remain unclear and unsolved. This paper illustrates the physical and statistical meaning of steady DCGs, and presents a method to calculate the JPD with local data, given that all variables are in a known single-valued Dynamic Uncertain Causality Graph(S-DUCG), and thus defines a new Bayesian Network with steady DCGs. The so-called single-valued means that only the causes of the true state of a variable are specified, while the false state is the complement of the true state.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
基金supported by the National Natural Science Foundation of China under Grant 71671103
文摘It is desired to obtain the joint probability distribution(JPD) over a set of random variables with local data, so as to avoid the hard work to collect statistical data in the scale of all variables. A lot of work has been done when all variables are in a known directed acyclic graph(DAG). However, steady directed cyclic graphs(DCGs) may be involved when we simply combine modules containing local data together, where a module is composed of a child variable and its parent variables. So far, the physical and statistical meaning of steady DCGs remain unclear and unsolved. This paper illustrates the physical and statistical meaning of steady DCGs, and presents a method to calculate the JPD with local data, given that all variables are in a known single-valued Dynamic Uncertain Causality Graph(S-DUCG), and thus defines a new Bayesian Network with steady DCGs. The so-called single-valued means that only the causes of the true state of a variable are specified, while the false state is the complement of the true state.
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]）.
