53,768 research outputs found
Optimal Linear Arrangement of Interval Graphs
http://www.springerlink.com/content/wrk8346657167528/?p=a1f283d79ac14affb4d165501b84e569&pi=23We study the optimal linear arrangement (OLA) problem on interval graphs. Several linear layout problems that are NP-hard on general graphs are solvable in polynomial time on interval graphs.We prove that, quite surprisingly, optimal linear arrangement of interval graphs is NP-hard. The same result holds for permutation graphs. We present a lower bound and a simple and fast 2-approximation algorithm based on any interval model of the input graph
Theoretical Foundations of Autoregressive Models for Time Series on Acyclic Directed Graphs
Three classes of models for time series on acyclic directed graphs are considered. At first a review of tree-structured models constructed from a nested partitioning of the observation interval is given. This nested partitioning leads to several resolution scales. The concept of mass balance allowing to interpret the average over an interval as the sum of averages over the sub-intervals implies linear restrictions in the tree-structured model. Under a white noise assumption for transition and observation noise there is an change-of-resolution Kalman filter for linear least squares prediction of interval averages \shortcite{chou:1991}. This class of models is generalized by modeling transition noise on the same scale in linear state space form. The third class deals with models on a more general class of directed acyclic graphs where nodes are allowed to have two parents. We show that these models have a linear state space representation with white system and coloured observation noise
Some results on triangle partitions
We show that there exist efficient algorithms for the triangle packing
problem in colored permutation graphs, complete multipartite graphs,
distance-hereditary graphs, k-modular permutation graphs and complements of
k-partite graphs (when k is fixed). We show that there is an efficient
algorithm for C_4-packing on bipartite permutation graphs and we show that
C_4-packing on bipartite graphs is NP-complete. We characterize the cobipartite
graphs that have a triangle partition
Rainbow domination and related problems on some classes of perfect graphs
Let and let be a graph. A function is a rainbow function if, for every vertex with
, . The rainbow domination number
is the minimum of over all rainbow
functions. We investigate the rainbow domination problem for some classes of
perfect graphs
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