Query by String word spotting based on character bi-gram indexing

In this paper we propose a segmentation-free query by string word spotting method. Both the documents and query strings are encoded using a recently proposed word representa- tion that projects images and strings into a common atribute space based on a pyramidal histogram of characters(PHOC). These attribute models are learned using linear SVMs over the Fisher Vector representation of the images along with the PHOC labels of the corresponding strings. In order to search through the whole page, document regions are indexed per character bi- gram using a similar attribute representation. On top of that, we propose an integral image representation of the document using a simplified version of the attribute model for efficient computation. Finally we introduce a re-ranking step in order to boost retrieval performance. We show state-of-the-art results for segmentation-free query by string word spotting in single-writer and multi-writer standard datasetsComment: To be published in ICDAR201

Linear Time Subgraph Counting, Graph Degeneracy, and the Chasm at Size Six

We consider the problem of counting all k-vertex subgraphs in an input graph, for any constant k. This problem (denoted SUB-CNT_k) has been studied extensively in both theory and practice. In a classic result, Chiba and Nishizeki (SICOMP 85) gave linear time algorithms for clique and 4-cycle counting for bounded degeneracy graphs. This is a rich class of sparse graphs that contains, for example, all minor-free families and preferential attachment graphs. The techniques from this result have inspired a number of recent practical algorithms for SUB-CNT_k. Towards a better understanding of the limits of these techniques, we ask: for what values of k can SUB_CNT_k be solved in linear time? We discover a chasm at k=6. Specifically, we prove that for k < 6, SUB_CNT_k can be solved in linear time. Assuming a standard conjecture in fine-grained complexity, we prove that for all k ? 6, SUB-CNT_k cannot be solved even in near-linear time