We consider dynamic data structures in which updates rebuild a static solution. Space bounds for persistent versions of these structures can often be reduced by using an offline persistent data structure in place of the static solution. We apply this technique to decomposable search problems, to dynamic linear programming, and to maintaining the minimum spanning tree in a dynamic graph. Our alg...

Over recent years Dirichlet processes and the associated Chinese restaurant process (CRP) have found many applications in clustering while the Indian buffet process (IBP) is increasingly used to describe latent feature models. These models are attractive because they ensure exchangeability (over samples). We propose here extensions of these models where the dependency between samples is given b...

We consider a graph Ln, with n even, which is a complete graph with an additional loop at each vertex and minus 1-factor and we prove that it is edge-disjointly decomposable into closed trails of even lengths greater than four, whenever these lengths sum up to the size of the graph Ln. We also show that this statement remains true if we remove from Ln two loops attached to nonadjacent vertices....

We say that two graphs G1 and G2 with the same vertex set commute if their adjacency matrices commute. In this paper, we find all integers n such that the complete bipartite graph Kn, n is decomposable into commuting perfect matchings or commuting Hamilton cycles. We show that there are at most n−1 linearly independent commuting adjacency matrices of size n; and if this bound occurs, then there...

In this article we study the simultaneous estimation of the means in Poisson decomposable graphical models. We derive some classes of estimators which improve on the maximum likelihood estimator under the normalized squared losses. Our estimators are based on the argument in Chou[3] and shrink the maximum likelihood estimator depending on the marginal frequencies of variables forming a complete...

Abstract An m-factorization of a graph is a decomposition of its edge set into edge-disjoint m-regular spanning subgraphs (or factors). In this paper, we prove the existence of an isomorphic m-factorization of the Cartesian product of graphs each of which is decomposable into Hamiltonian even cycles. Moreover, each factor in the m-factorization is m-connected, and bipancyclic for m ≥ 4 and near...

Algorithmic decidability is established for two order-theoretic properties of downward closed subsets defined by finitely many obstructions in infinite posets. The under consideration are (a) being atomic, i.e., not decomposable as a union proper or, equivalently, satisfying the joint embedding property; and (b) well quasi-ordered. posets (1) words over finite alphabet consecutive subword order...

We continue to study Cayley configuration spaces of 1-degree-of-freedom (1-dof) linkages in 2D begun in Part I of this paper, i.e. the set of attainable lengths for a non-edge. In Part II, we focus on the algebraic complexity of describing endpoints of the intervals in the set, i.e., the Cayley complexity. Specifically, we focus on Cayley configuration spaces of a natural class of 1-dof linkage...

In this study we present a sequential sampling methodology for Bayesian inference in decomposable graphical models. We recast the problem of graph estimation, which in general lacks natural sequential interpretation, into a sequential setting. Specifically, we propose a recursive Feynman-Kac model which generates a flow of junction tree distributions over a space of increasing dimensions and de...