29,151 research outputs found
Extremal Infinite Graph Theory
We survey various aspects of infinite extremal graph theory and prove several
new results. The lead role play the parameters connectivity and degree. This
includes the end degree. Many open problems are suggested.Comment: 41 pages, 16 figure
Extended Dijkstra algorithm and Moore-Bellman-Ford algorithm
Study the general single-source shortest path problem. Firstly, define a path
function on a set of some path with same source on a graph, and develop a kind
of general single-source shortest path problem (GSSSP) on the defined path
function. Secondly, following respectively the approaches of the well known
Dijkstra's algorithm and Moore-Bellman-Ford algorithm, design an extended
Dijkstra's algorithm (EDA) and an extended Moore-Bellman-Ford algorithm (EMBFA)
to solve the problem GSSSP under certain given conditions. Thirdly, introduce a
few concepts, such as order-preserving in last road (OPLR) of path function,
and so on. And under the assumption that the value of related path function for
any path can be obtained in time, prove respectively the algorithm EDA
solving the problem GSSSP in time and the algorithm EMBFA solving
the problem GSSSP in time. Finally, some applications of the
designed algorithms are shown with a few examples. What we done can improve
both the researchers and the applications of the shortest path theory.Comment: 25 page
Minimum congestion spanning trees in planar graphs
The main purpose of the paper is to develop an approach to evaluation or
estimation of the spanning tree congestion of planar graphs. This approach is
used to evaluate the spanning tree congestion of triangular grids
Turaev genus, knot signature, and the knot homology concordance invariants
We give bounds on knot signature, the Ozsvath-Szabo tau invariant, and the
Rasmussen s invariant in terms of the Turaev genus of the knot.Comment: 15 pages, 5 figure
Enhancing Domain Word Embedding via Latent Semantic Imputation
We present a novel method named Latent Semantic Imputation (LSI) to transfer
external knowledge into semantic space for enhancing word embedding. The method
integrates graph theory to extract the latent manifold structure of the
entities in the affinity space and leverages non-negative least squares with
standard simplex constraints and power iteration method to derive spectral
embeddings. It provides an effective and efficient approach to combining entity
representations defined in different Euclidean spaces. Specifically, our
approach generates and imputes reliable embedding vectors for low-frequency
words in the semantic space and benefits downstream language tasks that depend
on word embedding. We conduct comprehensive experiments on a carefully designed
classification problem and language modeling and demonstrate the superiority of
the enhanced embedding via LSI over several well-known benchmark embeddings. We
also confirm the consistency of the results under different parameter settings
of our method.Comment: ACM SIGKDD 201
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