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Graph-encoded maps

Sóstenes Lins
1982 Journal of combinatorial theory. Series B (Print)  
An edge-colored graph model for the study of finite graphs embedded in surfaces (maps) is presented.  ...  Moreover, the orientability of the surface of a map is shown to be equivalent to the bipartiteness of the colored graph. * Supported by UFPE and FINEP.  ...  GEMS AND MAPS The term "gem" is an acronym for "graph-encoded map."  ... 
doi:10.1016/0095-8956(82)90033-8 fatcat:5abiits5pzaphf75uy5oe5o56u

Short encodings of planar graphs and maps

Kenneth Keeler, Jeffery Westbrook
1995 Discrete Applied Mathematics  
We discuss space-efficient encoding schemes for planar graphs and maps. Our results improve on the constants of previous schemes and can be achieved with simple encoding algorithms.  ...  Each map is an embedding of a unique graph, but a given graph may have multiple embeddings. Hence maps must require more bits to encode than graphs in some average sense.  ...  All maps and graphs to be encoded in the rest of this paper shall be understood to be unlabeled and connected. We show encodings for loop-and stick-free maps and graphs in 3 bits per edge.  ... 
doi:10.1016/0166-218x(93)e0150-w fatcat:ergpesoz3zcfhcdrshey2z7kui

Directed Acyclic Graph Encoding for Compressed Shadow Maps

Leonardo Scandolo, Elmar Eisemann
2021
It builds upon compressed precomputed multiresolution hierarchies but uses a directed acyclic graph to encode its tree structure.  ...  Further, depth values are compressed and stored separately and we use a bit-plane encoding for the lower tree levels entries in order to further reduce memory requirements and increase locality.  ...  Our Method We create a dual shadow map [WE03] , encoding the first and second surface as seen from the light source.  ... 
doi:10.2312/hpg.20211283 fatcat:e63yutgshbfq7pgrtln6jo5lpi

Encoding and Selecting Coarse-Grain Mapping Operators with Hierarchical Graphs [article]

Maghesree Chakraborty, Chenliang Xu, Andrew D. White
2018 pre-print
The resulting number of mapping operators is still large, so we introduce hierarchical graphs which encode multiple CG mapping operators.  ...  The encoding method is demonstrated for methanol and a 14-mer peptide. This encoding provides a foundation to perform automated mapping selection.  ...  Hierarchical Graphs Encoding Mapping Operators We will introduce two forms of hierarchical graphs: the mapping operator tree (MOT) and the mapping operator graph (MOG).  ... 
doi:10.1063/1.5040114 arXiv:1804.04997v1 fatcat:i6iwwgnkrzg2liy4rxv6hvavum

Encoding and Querying Historic Map Content [chapter]

Simon Scheider, Jim Jones, Alber Sánchez, Carsten Keßler
2014 Lecture Notes in Geoinformation and Cartography  
Libraries have large collections of map documents with rich spatiotemporal information encoded in the visual representation of the map.  ...  We suggest ways to formally encode historic map content in an approximate intensional manner which still allows useful queries.  ...  Note that this "something" needs to be a graph in our case: Each map represents one graph which encodes its content, see Fig. 4 .  ... 
doi:10.1007/978-3-319-03611-3_15 fatcat:b2gkjjndknc3jlgu35wxfpovhe

UNISON: Unpaired Cross-Lingual Image Captioning

Jiahui Gao, Yi Zhou, Philip L. H. Yu, Shafiq Joty, Jiuxiang Gu
2022 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
in the scene graph encoding space and decode sentences in the target language, and (2) a cross-modal unsupervised feature mapping, which seeks to map the encoded scene graph features from image modality  ...  Specifically, our method consists of two phases: (1) a cross-lingual auto-encoding process, which utilizing a sentence parallel (bitext) corpus to learn the mapping from the source to the target language  ...  GM WORD maps the English scene graph to Chinese through word-level mapping in the scene graph encoding space.  ... 
doi:10.1609/aaai.v36i10.21310 fatcat:sc5ty4b275bntgeultpbocy7h4

Unpaired Image Captioning via Scene Graph Alignments [article]

Jiuxiang Gu, Shafiq Joty, Jianfei Cai, Handong Zhao, Xu Yang, Gang Wang
2019 arXiv   pre-print
Our framework comprises an image scene graph generator, a sentence scene graph generator, a scene graph encoder, and a sentence decoder.  ...  Specifically, we first train the scene graph encoder and the sentence decoder on the text modality.  ...  Our framework comprises an image scene graph generator, a sentence scene graph generator, a scene graph encoder, a sentence decoder, and a feature alignment module that maps the features from image to  ... 
arXiv:1903.10658v4 fatcat:escnrteqzbhmdanzulps3xtrwa

GRPE: Relative Positional Encoding for Graph Transformer [article]

Wonpyo Park, Woonggi Chang, Donggeon Lee, Juntae Kim, Seung-won Hwang
2022 arXiv   pre-print
We name our method Graph Relative Positional Encoding dedicated to graph representation learning.  ...  Designing an efficient model to encode graphs is a key challenge of molecular representation learning.  ...  Our two relative positional encodings, spatial encoding and edge encoding, are used to encode graph on both attention map and value.  ... 
arXiv:2201.12787v2 fatcat:2lbdhhe47vcitbc4rhg25dv5sq

Unpaired Image Captioning via Scene Graph Alignments

Jiuxiang Gu, Shafiq Joty, Jianfei Cai, Handong Zhao, Xu Yang, Gang Wang
2019 2019 IEEE/CVF International Conference on Computer Vision (ICCV)  
Our framework comprises an image scene graph generator, a sentence scene graph generator, a scene graph encoder, and a sentence decoder.  ...  Specifically, we first train the scene graph encoder and the sentence decoder on the text modality.  ...  Our framework comprises an image scene graph generator, a sentence scene graph generator, a scene graph encoder, a sentence decoder, and a feature alignment module that maps the features from image to  ... 
doi:10.1109/iccv.2019.01042 dblp:conf/iccv/GuJCZYW19 fatcat:sheuqcch7zgnbg52burco6wqv4

The Design Space of Temporal Graph Visualisation [article]

Natalie Kerracher, Jessie Kennedy, Kevin Chalmers
2014 Eurographics Conference on Visualization  
This paper presents our work in mapping the design space of techniques for temporal graph visualisation.  ...  Weidentify two independent dimensions upon which the techniques can be classified: graph structural encoding andtemporal encoding.  ...  of graph structural and temporal encodings.  ... 
doi:10.2312/eurovisshort.20141149 dblp:conf/vissym/KerracherKC14 fatcat:m5qv77cubnfq5czrzxlepbzjpa

UNISON: Unpaired Cross-lingual Image Captioning [article]

Jiahui Gao, Yi Zhou, Philip L. H. Yu, Shafiq Joty, Jiuxiang Gu
2022 arXiv   pre-print
in the scene graph encoding space and decode sentences in the target language, and (ii) a cross-modal unsupervised feature mapping, which seeks to map the encoded scene graph features from image modality  ...  Specifically, our method consists of two phases: (i) a cross-lingual auto-encoding process, which utilizing a sentence parallel (bitext) corpus to learn the mapping from the source to the target language  ...  For crosslingual auto-encoding, we collect a paired English-Chinese corpus from existing MT datasets, including WMT19 (Barrault et al. 2019), AIC MT (Wu et al. 2017) , UM (Tian et al. 2014) , and Trans-zh  ... 
arXiv:2010.01288v3 fatcat:byutcnokejfrbm4cdcluyjjn7a

Contains and inside relationships within combinatorial pyramids

Luc Brun, Walter Kropatsch
2006 Pattern Recognition  
The different graph models used within the irregular pyramid framework encode different types of relationships between regions.  ...  Irregular pyramids are made of a stack of successively reduced graphs embedded in the plane. Such pyramids are used within the segmentation framework to encode a hierarchy of partitions.  ...  Combinatorial maps A 2D combinatorial map may be understood as a planar graph encoding explicitly the orientation in the plane.  ... 
doi:10.1016/j.patcog.2005.10.015 fatcat:hb3ie3iuurb4dnl7vraqfg3jzq

Joint learning of object graph and relation graph for visual question answering [article]

Hao Li, Xu Li, Belhal Karimi, Jie Chen, Mingming Sun
2022 arXiv   pre-print
In this paper, we introduce a novel Dual Message-passing enhanced Graph Neural Network (DM-GNN), which can obtain a balanced representation by properly encoding multi-scale scene graph information.  ...  Specifically, we (i)transform the scene graph into two graphs with diversified focuses on objects and relations; Then we design a dual structure to encode them, which increases the weights from relations  ...  After T steps, the encoder generates the final hidden state map G of the graph.  ... 
arXiv:2205.04188v1 fatcat:6gickhmifvft5p3e4ii4pe777y

Contraction kernels and combinatorial maps

Luc Brun, Walter Kropatsch
2003 Pattern Recognition Letters  
Compared to usual graph data structures, combinatorial maps offer an explicit encoding of the orientation of edges around vertices.  ...  The graphs used in the pyramid may be region adjacency graphs, dual graphs or combinatorial maps.  ...  Combinatorial maps A combinatorial map (Gareth and Singerman, 1978) may be understood as a planar graph encoding explicitly the orientation of edges around a given vertex.  ... 
doi:10.1016/s0167-8655(02)00251-9 fatcat:zbk2zy6rv5cefbfvm2iwru6ubu

ReCoG: A Deep Learning Framework with Heterogeneous Graph for Interaction-Aware Trajectory Prediction [article]

Xiaoyu Mo and Yang Xing and Chen Lv
2020 arXiv   pre-print
encoded using Convolutional Neural Network (CNN).  ...  Nodes in the graph contain corresponding features, where a vehicle node contains its sequential feature encoded using Recurrent Neural Network (RNN), and an infrastructure node contains spatial feature  ...  graph, which contains two kinds of nodes, the vehicle node and the map node.  ... 
arXiv:2012.05032v1 fatcat:qn4nshkjyngijb7zsarfafzjwy
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