The Node Vector Distance Problem in Complex Networks

We describe a problem in complex networks we call the Node Vector Distance (NVD) problem, and we survey algorithms currently able to address it. Complex networks are a useful tool to map a non-triv...

[1]  Martin Rumpf,et al.  Computation of optimal transport on discrete metric measure spaces , 2017, Numerische Mathematik.

[2]  Anton Andreychuk,et al.  Any-Angle Pathfinding for Multiple Agents Based on SIPP Algorithm , 2017, ICAPS.

[3]  Kostas E. Bekris,et al.  Scalable asymptotically-optimal multi-robot motion planning , 2017, 2017 International Symposium on Multi-Robot and Multi-Agent Systems (MRS).

[4]  Maria L. Gini,et al.  Adaptive Learning for Multi-Agent Navigation , 2015, AAMAS.

[5]  Frank L. Lewis,et al.  Solutions for Multiagent Pursuit-Evasion Games on Communication Graphs: Finite-Time Capture and Asymptotic Behaviors , 2020, IEEE Transactions on Automatic Control.

[6]  Aurélien Garivier,et al.  On the Complexity of Best-Arm Identification in Multi-Armed Bandit Models , 2014, J. Mach. Learn. Res..

[7]  Mauro Dell'Amico,et al.  Assignment Problems , 1998, IFIP Congress: Fundamentals - Foundations of Computer Science.

[8]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[9]  Paul Van Dooren,et al.  A MEASURE OF SIMILARITY BETWEEN GRAPH VERTICES . WITH APPLICATIONS TO SYNONYM EXTRACTION AND WEB SEARCHING , 2002 .

[10]  Ron Boschma,et al.  Agents of Structural Change: The Role of Firms and Entrepreneurs in Regional Diversification , 2018 .

[11]  César A. Hidalgo,et al.  The Product Space Conditions the Development of Nations , 2007, Science.

[12]  Ira Assent,et al.  Approximation Techniques for Indexing the Earth Mover’s Distance in Multimedia Databases , 2006, 22nd International Conference on Data Engineering (ICDE'06).

[13]  Alexander J. Smola,et al.  Trend Filtering on Graphs , 2014, J. Mach. Learn. Res..

[14]  William E. Winkler,et al.  String Comparator Metrics and Enhanced Decision Rules in the Fellegi-Sunter Model of Record Linkage. , 1990 .

[15]  Harry Eugene Stanley,et al.  Catastrophic cascade of failures in interdependent networks , 2009, Nature.

[16]  Donald F. Towsley,et al.  The effect of network topology on the spread of epidemics , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[17]  Sunil K. Narang,et al.  Localized iterative methods for interpolation in graph structured data , 2013, 2013 IEEE Global Conference on Signal and Information Processing.

[18]  Pavel Surynek,et al.  Compact Representations of Cooperative Path-Finding as SAT Based on Matchings in Bipartite Graphs , 2014, 2014 IEEE 26th International Conference on Tools with Artificial Intelligence.

[19]  E. David,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World , 2010 .

[20]  Douglas B. Kell,et al.  Understanding the foundations of the structural similarities between marketed drugs and endogenous human metabolites , 2015, Front. Pharmacol..

[21]  Pierre Vandergheynst,et al.  Vertex-Frequency Analysis on Graphs , 2013, ArXiv.

[22]  Nathan R. Sturtevant,et al.  Extended Increasing Cost Tree Search for Non-Unit Cost Domains , 2018, IJCAI.

[23]  Matthew A. Jaro,et al.  Advances in Record-Linkage Methodology as Applied to Matching the 1985 Census of Tampa, Florida , 1989 .

[24]  Wotao Yin,et al.  A Parallel Method for Earth Mover’s Distance , 2018, J. Sci. Comput..

[25]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[26]  László Babai,et al.  Graph isomorphism in quasipolynomial time [extended abstract] , 2015, STOC.

[27]  Neil Swainston,et al.  A ‘rule of 0.5’ for the metabolite-likeness of approved pharmaceutical drugs , 2014, Metabolomics.

[28]  Michael Werman,et al.  A Linear Time Histogram Metric for Improved SIFT Matching , 2008, ECCV.

[29]  Douglas B Kell,et al.  Implications of the dominant role of transporters in drug uptake by cells. , 2009, Current topics in medicinal chemistry.

[30]  David J. Galas,et al.  Expansion of the Kullback-Leibler Divergence, and a new class of information metrics , 2017, Axioms.

[31]  A. Balmann Farm-Based Modelling of Regional Structural Change: A Cellular Automata Approach , 1997 .

[32]  Jon Kleinberg,et al.  The link prediction problem for social networks , 2003, CIKM '03.

[33]  José M. F. Moura,et al.  Discrete Signal Processing on Graphs: Frequency Analysis , 2013, IEEE Transactions on Signal Processing.

[34]  Andrew McGregor,et al.  Sketching Earth-Mover Distance on Graph Metrics , 2013, APPROX-RANDOM.

[35]  C. Givens,et al.  A class of Wasserstein metrics for probability distributions. , 1984 .

[36]  Steven M. LaValle,et al.  Multi-agent Path Planning and Network Flow , 2012, WAFR.

[37]  Chris Arney,et al.  The Atlas of Economic Complexity: Mapping Paths to Prosperity , 2012 .

[38]  Nathan R. Sturtevant,et al.  Using Hierarchical Constraints to Avoid Conflicts in Multi-Agent Pathfinding , 2017, ICAPS.

[39]  J. Köbler,et al.  The Graph Isomorphism Problem: Its Structural Complexity , 1993 .

[40]  Jon Kleinberg,et al.  Maximizing the spread of influence through a social network , 2003, KDD '03.

[41]  Arthur Cayley,et al.  The Collected Mathematical Papers: On Monge's “Mémoire sur la théorie des déblais et des remblais” , 2009 .

[42]  J. Maas Gradient flows of the entropy for finite Markov chains , 2011, 1102.5238.

[43]  C. Villani Topics in Optimal Transportation , 2003 .

[44]  Jiawei Han,et al.  gSpan: graph-based substructure pattern mining , 2002, 2002 IEEE International Conference on Data Mining, 2002. Proceedings..

[45]  Xuelong Li,et al.  A survey of graph edit distance , 2010, Pattern Analysis and Applications.

[46]  Jon M. Kleinberg,et al.  The link-prediction problem for social networks , 2007, J. Assoc. Inf. Sci. Technol..

[47]  Dinesh Manocha,et al.  The Hybrid Reciprocal Velocity Obstacle , 2011, IEEE Transactions on Robotics.

[48]  Michele Coscia,et al.  Generalized Euclidean Measure to Estimate Network Distances , 2020, ICWSM.

[49]  Vladimir I. Levenshtein,et al.  Binary codes capable of correcting deletions, insertions, and reversals , 1965 .

[50]  Beom Jun Kim,et al.  Growing scale-free networks with tunable clustering. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

[52]  Jure Leskovec,et al.  Friendship and mobility: user movement in location-based social networks , 2011, KDD.

[53]  Sven Koenig,et al.  Multi-Agent Path Finding with Delay Probabilities , 2016, AAAI.

[54]  Narsingh Deo,et al.  Shortest-path algorithms: Taxonomy and annotation , 1984, Networks.

[55]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[56]  T. D. Parsons,et al.  Pursuit-evasion in a graph , 1978 .

[57]  Dino Pedreschi,et al.  A classification for community discovery methods in complex networks , 2011, Stat. Anal. Data Min..

[58]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[59]  Sven Koenig,et al.  Multi-Agent Path Finding for Large Agents , 2019, SOCS.

[60]  Antonio Ortega,et al.  Towards a sampling theorem for signals on arbitrary graphs , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[61]  Ron Boschma,et al.  How Do Regions Diversify over Time? Industry Relatedness and the Development of New Growth Paths in Regions , 2011 .

[62]  Chris Arney,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World (Easley, D. and Kleinberg, J.; 2010) [Book Review] , 2013, IEEE Technology and Society Magazine.

[63]  B. Alspach SEARCHING AND SWEEPING GRAPHS: A BRIEF SURVEY , 2006 .

[64]  Dimitrios M. Thilikos,et al.  An annotated bibliography on guaranteed graph searching , 2008, Theor. Comput. Sci..

[65]  F. Radicchi,et al.  Benchmark graphs for testing community detection algorithms. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[66]  Andrea Cavallaro,et al.  Automatic Analysis of Facial Affect: A Survey of Registration, Representation, and Recognition , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[67]  David Easley,et al.  Networks, Crowds, and Markets by David Easley , 2010 .

[68]  Preeti Kumari,et al.  ERROR DETECTING AND ERROR CORRECTING CODES , 2014 .

[69]  Evgueni A. Haroutunian,et al.  Information Theory and Statistics , 2011, International Encyclopedia of Statistical Science.

[70]  Jure Leskovec,et al.  The dynamics of viral marketing , 2005, EC '06.

[71]  Afshin Fassihi,et al.  The role of different sampling methods in improving biological activity prediction using deep belief network , 2017, J. Comput. Chem..

[72]  Rossano Schifanella,et al.  Link Creation and Profile Alignment in the aNobii Social Network , 2010, 2010 IEEE Second International Conference on Social Computing.

[73]  Pierre Vandergheynst,et al.  Wavelets on Graphs via Spectral Graph Theory , 2009, ArXiv.

[74]  George Karakostas,et al.  Faster approximation schemes for fractional multicommodity flow problems , 2008, TALG.

[75]  Montacer Essid,et al.  Quadratically-Regularized Optimal Transport on Graphs , 2017, SIAM J. Sci. Comput..

[76]  Kaspar Riesen,et al.  Approximate graph edit distance computation by means of bipartite graph matching , 2009, Image Vis. Comput..

[77]  Michele Coscia,et al.  Network Backboning with Noisy Data , 2017, 2017 IEEE 33rd International Conference on Data Engineering (ICDE).

[78]  Flaminia L. Luccio Intruder Capture in Sierpinski Graphs , 2007, FUN.

[79]  Leonidas J. Guibas,et al.  The Earth Mover's Distance as a Metric for Image Retrieval , 2000, International Journal of Computer Vision.

[80]  Edwin R. Hancock,et al.  Bayesian graph edit distance , 1999, Proceedings 10th International Conference on Image Analysis and Processing.

[81]  F. L. Hitchcock The Distribution of a Product from Several Sources to Numerous Localities , 1941 .

[82]  Michael Werman,et al.  A Unified Approach to the Change of Resolution: Space and Gray-Level , 1989, IEEE Trans. Pattern Anal. Mach. Intell..

[83]  Guido Caldarelli,et al.  A New Metrics for Countries' Fitness and Products' Complexity , 2012, Scientific Reports.

[84]  Anton Andreychuk,et al.  Multi-Agent Pathfinding with Continuous Time , 2019, IJCAI.

[85]  Matthew P Jacobson,et al.  Comparing Conformational Ensembles Using the Kullback-Leibler Divergence Expansion. , 2012, Journal of chemical theory and computation.

[86]  Norbert Krüger,et al.  Face recognition by elastic bunch graph matching , 1997, Proceedings of International Conference on Image Processing.

[87]  James Bailey,et al.  Information Theoretic Measures for Clusterings Comparison: Variants, Properties, Normalization and Correction for Chance , 2010, J. Mach. Learn. Res..

[88]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[89]  Jason M. O'Kane,et al.  Pursuit-evasion with fixed beams , 2016, 2016 IEEE International Conference on Robotics and Automation (ICRA).

[90]  Torsten Hoefler,et al.  Multi-agent Pathfinding with n Agents on Graphs with n Vertices: Combinatorial Classification and Tight Algorithmic Bounds , 2017, CIAC.

[91]  Kenneth M. Merz,et al.  Drug Design : Structure-and Ligand-Based Approaches , 2017 .

[92]  Leonidas J. Guibas,et al.  Continuous-Flow Graph Transportation Distances , 2016, ArXiv.

[93]  Elena Deza,et al.  Encyclopedia of Distances , 2014 .

[94]  Alessandro Vespignani,et al.  Epidemic dynamics and endemic states in complex networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[95]  Daniela Rus,et al.  Pebble Motion on Graphs with Rotations: Efficient Feasibility Tests and Planning Algorithms , 2012, WAFR.

[96]  Filippo Santambrogio,et al.  Optimal Transport for Applied Mathematicians , 2015 .

[97]  Alexander Kmentt 2017 , 2018, The Treaty Prohibiting Nuclear Weapons.

[98]  Howie Choset,et al.  Subdimensional expansion for multirobot path planning , 2015, Artif. Intell..

[99]  Oded Goldreich Finding the Shortest Move-Sequence in the Graph-Generalized 15-Puzzle Is NP-Hard , 2011, Studies in Complexity and Cryptography.

[100]  Stephan Kreutzer,et al.  Graph Searching Games and Width Measures for Directed Graphs , 2015, STACS.

[101]  Sven Koenig,et al.  Task and Path Planning for Multi-Agent Pickup and Delivery , 2019, AAMAS.

[102]  Rossano Schifanella,et al.  People Are Strange When You're a Stranger: Impact and Influence of Bots on Social Networks , 2012, ICWSM.

[103]  Horst Bunke,et al.  On a relation between graph edit distance and maximum common subgraph , 1997, Pattern Recognit. Lett..

[104]  Michael Werman,et al.  Fast and robust Earth Mover's Distances , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[105]  Nathan R. Sturtevant,et al.  Conflict-based search for optimal multi-agent pathfinding , 2012, Artif. Intell..

[106]  Douglas B. Kell,et al.  MetMaxStruct: A Tversky-Similarity-Based Strategy for Analysing the (Sub)Structural Similarities of Drugs and Endogenous Metabolites , 2016, Front. Pharmacol..

[107]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[108]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[109]  Gábor J. Székely,et al.  Hierarchical Clustering via Joint Between-Within Distances: Extending Ward's Minimum Variance Method , 2005, J. Classif..

[110]  Jaroslav Koča,et al.  A metric for graphs , 1986 .