Adjacency list

About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.

Planar Matching in Streams Revisited

Abstract: We present data stream algorithms for estimating the size or weight of the maximum matching in low arboricity graphs. A large body of work has focused on improving the constant approximation factor for general graphs when the data stream algorithm is permitted O(n polylog n) space where n is the number of nodes. This space is necessary if the algorithm must return the matching. Recently, Esfandiari et al. (SODA 2015) showed that it was possible to estimate the maximum cardinality of a matching in a planar graph up to a factor of 24+epsilon using O(epsilon^{-2} n^{2/3} polylog n) space. We first present an algorithm (with a simple analysis) that improves this to a factor 5+epsilon using the same space. We also improve upon the previous results for other graphs with bounded arboricity. We then present a factor 12.5 approximation for matching in planar graphs that can be implemented using O(log n) space in the adjacency list data stream model where the stream is a concatenation of the adjacency lists of the graph. The main idea behind our results is finding "local" fractional matchings, i.e., fractional matchings where the value of any edge e is solely determined by the edges sharing an endpoint with e. Our work also improves upon the results for the dynamic data stream model where the stream consists of a sequence of edges being inserted and deleted from the graph. We also extend our results to weighted graphs, improving over the bounds given by Bury and Schwiegelshohn (ESA 2015), via a reduction to the unweighted problem that increases the approximation by at most a factor of two.

LTL Planning for Groups of Robots

Abstract: We approach the general problem of planning and controlling groups of robots from logical and temporal specifications over regions of interest in 2D or 3D environments. The focus of this paper is on planning, and, enabled by our previous results, we assume that the environment is partitioned and described in the form of a graph whose nodes label the partition regions and whose edges capture adjacency relations among these regions. We also assume that the robots can synchronize when penetrating from a region to another. We develop a fully automated framework for generation of robot plans from robot abstract task specifications given in terms of linear temporal logic (LTL) formulas over regions of interest. Inter-robot collision avoidance is guaranteed, and the assignment of plans to specific robots is automatic. The main tools underlying our framework are model checking and bisimilarity equivalence relations

Text line segmentation using a fully convolutional network in handwritten document images

Abstract: Line detection in handwritten documents is an important problem for processing of scanned documents. While existing approaches mainly use hand-designed features or heuristic rules to estimate the location of text lines, the authors present a novel approach that trains a fully convolutional network (FCN) to predict text line structure in document images. A rough estimation of text line, or a line map, is obtained by using FCN, from which text strings that pass through characters in each text line are constructed. Finally, the touching characters should be separated and assigned to different text lines to complete the segmentation, for which line adjacency graph is used. Experimental results on ICDAR2013 Handwritten Segmentation Contest data set show high performance together with the robustness of the system with different types of languages and multi-skewed text lines.