4,581 research outputs found
Hypotheses testing on infinite random graphs
Drawing on some recent results that provide the formalism necessary to
definite stationarity for infinite random graphs, this paper initiates the
study of statistical and learning questions pertaining to these objects.
Specifically, a criterion for the existence of a consistent test for complex
hypotheses is presented, generalizing the corresponding results on time series.
As an application, it is shown how one can test that a tree has the Markov
property, or, more generally, to estimate its memory
Simple DFS on the Complement of a Graph and on Partially Complemented Digraphs
A complementation operation on a vertex of a digraph changes all outgoing
arcs into non-arcs, and outgoing non-arcs into arcs. A partially complemented
digraph is a digraph obtained from a sequence of vertex
complement operations on . Dahlhaus et al. showed that, given an
adjacency-list representation of , depth-first search (DFS) on
can be performed in time, where is the number of
vertices and is the number of edges in . To
achieve this bound, their algorithm makes use of a somewhat complicated
stack-like data structure to simulate the recursion stack, instead of
implementing it directly as a recursive algorithm. We give a recursive
algorithm that uses no complicated data-structures
Orderly Spanning Trees with Applications
We introduce and study the {\em orderly spanning trees} of plane graphs. This
algorithmic tool generalizes {\em canonical orderings}, which exist only for
triconnected plane graphs. Although not every plane graph admits an orderly
spanning tree, we provide an algorithm to compute an {\em orderly pair} for any
connected planar graph , consisting of a plane graph of , and an
orderly spanning tree of . We also present several applications of orderly
spanning trees: (1) a new constructive proof for Schnyder's Realizer Theorem,
(2) the first area-optimal 2-visibility drawing of , and (3) the best known
encodings of with O(1)-time query support. All algorithms in this paper run
in linear time.Comment: 25 pages, 7 figures, A preliminary version appeared in Proceedings of
the 12th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2001),
Washington D.C., USA, January 7-9, 2001, pp. 506-51
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