1887353
An Application of Well-Orderly Trees in Graph Drawing
Well-orderly trees seem to have the potential of becoming a powerful technique capable of deriving new results in graph encoding, graph enumeration and graph generation [3, 4]. In this paper, we reduce the height of the visibility representation of plane graphs from 5n/6 to (4n–1)/5, by using well-orderly trees.
39496103
An Application of Well-orderly Trees in Graph Drawing
Well-orderly tree is a powerful technique capable of deriving new results in graph encoding, graph enumeration and graph generation [3, 5]. In this paper, by using well-orderly trees, we prove that any plane graph G with n vertices has a visibility representation with height , which can be constructed in linear time. This improves the best previous bound of .
2506060
Synchronous Binarization for Machine Translation
Systems based on synchronous grammars and tree transducers promise to improve the quality of statistical machine translation output, but are often very computationally intensive. The complexity is exponential in the size of individual grammar rules due to arbitrary re-orderings between the two languages, and rules extracted from parallel corpora can be quite large. We devise a linear-time algorithm for factoring syntactic re-orderings by binarizing synchronous rules when possible and show that the resulting rule set significantly improves the speed and accuracy of a state-of-the-art syntax-based machine translation system.
8195983
Poisson shape interpolation
In this paper, we propose a novel shape interpolation approach based on Poisson equation. We formulate the trajectory problem of shape interpolation as solving Poisson equations defined on a domain mesh. A non-linear gradient field interpolation method is proposed to take both vertex coordinates and surface orientation into account. With proper boundary conditions, the in-between shapes are reconstructed implicitly from the interpolated gradient fields, while traditional methods usually manipulate vertex coordinates directly. Besides of global shape interpolation, our method is also applicable to local shape interpolation, and can be further enhanced by incorporating with deformation. Our approach can generate visual pleasing and physical plausible morphing sequences with stable area and volume changes. Experimental results demonstrate that our technique can avoid the shrinkage problem appeared in linear shape interpolation.
15887745
The Rotation Graphs of Perfect Matchings of Plane Bipartite Graphs
Abstract In the present paper, the minimal proper alternating cycle (MPAC) rotation graph R(G) of perfect matchings of a plane bipartite graph G is defined. We show that an MPAC rotation graph R(G) of G is a directed rooted tree, and thus extend such a result for generalized polyhex graphs to arbitrary plane bipartite graphs. As an immediate result, we describe a one-to-one correspondence between MPAC systems and perfect matchings in G.
139220
Representational Upper Bounds of Bayesian Networks
One of the fundamental issues of Bayesian networks is their representational power, re-ecting what kind of functions they can or cannot represent. In this paper, we rst prove an upper bound on the representational power of Augmented Naive Bayes. We then extend the result to general Bayesian networks. Roughly speaking, if a function contains an m-XOR, there exists no Bayesian networks with node having at most m ? 1 parents to represent it.
7092740
Representing Conditional Independence Using Decision Trees
While the representation of decision trees is fully expressive theoretically, it has been observed that traditional decision trees has the replication problem. This problem makes decision trees to be large and learnable only when sufficient training data are available. In this paper, we present a new representation model, conditional independence trees (CITrees), to tackle the replication problem from probability perspective. We propose a novel algorithm for learning CITrees. Our experiments show that CITrees outperform naive Bayes (Langley, Iba, & Thomas 1992), C4.5 (Quinlan 1993), TAN (Friedman, Geiger, & Goldszmidt 1997), and AODE (Webb, Boughton, & Wang 2005) significantly in classification accuracy.