A Sequential Importance Sampling Algorithm for Counting Linear Extensions
نویسندگان
چکیده
منابع مشابه
Counting Linear Extensions of a Partial Order
A partially ordered set (P,<) is a set P together with an irreflexive, transitive relation. A linear extension of (P,<) is a relation (P,≺) such that (1) for all a, b ∈ P either a ≺ b or a = b or b ≺ a, and (2) if a < b then a ≺ b; in other words, a total order that preserves the original partial order. We define Λ(P ) as the set of all linear extensions of P , and define N(P ) = |Λ(P )|. Throu...
متن کاملSequential Importance Sampling for Multiway Tables
We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates sampling values at each step to properties of the associated toric ideal using computational commutative algebra. In particular, the property of interval cell c...
متن کاملSequential Importance Sampling for Visual Tracking Reconsidered
We consider the task of filtering dynamical systems observed in noise by means of sequential importance sampling when the proposal is restricted to the innovation components of the state. It is argued that the unmodified sequential importance sampling/resampling (SIR) algorithm may yield high variance estimates of the posterior in this case, resulting in poor performance when e.g. in visual tra...
متن کاملCounting Linear Extensions: Parameterizations by Treewidth
We consider the #P-complete problem of counting the number of linear extensions of a poset (#LE); a fundamental problem in order theory with applications in a variety of distinct areas. In particular, we study the complexity of #LE parameterized by the well-known decompositional parameter treewidth for two natural graphical representations of the input poset, i.e., the cover and the incomparabi...
متن کاملCounting Linear Extensions of Sparse Posets
Counting the linear extensions of a partially ordered set (poset) is a fundamental problem with several applications. We present two exact algorithms that target sparse posets in particular. The first algorithm breaks the counting task into subproblems recursively. The second algorithm uses variable elimination via inclusion–exclusion and runs in polynomial time for posets with a cover graph of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ACM Journal of Experimental Algorithmics
سال: 2020
ISSN: 1084-6654,1084-6654
DOI: 10.1145/3385650