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A path algebra for multi-relational graphs

Marko A. Rodriguez, Peter Neubauer
2011 2011 IEEE 27th International Conference on Data Engineering Workshops  
This article defines an algebra for traversing such graphs that is based on an n-ary relational algebra, a concatenative single-relational path algebra, and a tensor-based multi-relational algebra.  ...  The presented algebra provides a monoid, automata, and formal language theoretic foundation for the construction of a multi-relational graph traversal engine.  ...  CONCLUSION This article defined a path algebra for multi-relational graphs represented as G = (V, E ⊆ (V × Ω × V ).  ... 
doi:10.1109/icdew.2011.5767613 dblp:conf/icde/RodriguezN11 fatcat:pdcwqcjijbapbgbjxtwm5byrhe

Towards a Unified Theory of Policy-Based Routing

C.-K. Chau, R. Gibbens, T. G. Griffin
2006 Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications  
We use the term policy-based routing to refer collectively to the Stable Paths Problem, Sobrinho's Routing Algebras, and to classical Path Algebras (semi-rings used to generalise minimum-weight routing  ...  These theories all contain sufficient conditions that ensure the existence of solutions (stable routings) for labelled graphs.  ...  Chi-kin Chau is grateful to The Croucher Foundation for financial support. Richard Gibbens acknowledges support from EPSRC grant GR/S86266/01.  ... 
doi:10.1109/infocom.2006.125 dblp:conf/infocom/ChauGG06 fatcat:m3o4nzf3wbbjznyrew3qfpw4ue

Exposing multi-relational networks to single-relational network analysis algorithms

Marko A. Rodriguez, Joshua Shinavier
2010 Journal of Informetrics  
This article presents an algebra for mapping multi-relational networks to single-relational networks, thereby exposing them to single-relational network analysis algorithms.  ...  While multi-relational networks are more expressive in terms of the variety of relationships they can capture, there is a need for a general framework for transferring the many single-relational network  ...  Relationship to Multi-Relational Graph Query Languages The presented path algebra has many similarities to graph query languages such as GraphLog [26] , Path Query Language (PQL) [27] , and SPARQL Protocol  ... 
doi:10.1016/j.joi.2009.06.004 fatcat:su5gbkoiljhbfjgnxiuezifymq

Generalized Zeon Algebras: Theory and Application to Multi-Constrained Path Problems

René Schott, G. Stacey Staples
2015 Advances in Applied Clifford Algebras  
As an application, an operator calculus approach to multi-constrained path problems is described. keywords: shortest paths, message routing, operator calculus, semigroup algebras MSC: 68W30, 81R05  ...  The inherent combinatorial properties of generalized zeons make them useful for routing problems by implicitly pruning the underlying tree structures.  ...  The entries of this matrix are the null-square generators of a zeon algebra of appropriate dimension for the graph.  ... 
doi:10.1007/s00006-015-0595-0 fatcat:7dzddtwxdzacncddydllzasagm

Solving multi-metric network problems: An interplay between idempotent semiring rules

Kiran K. Somasundaram, John S. Baras
2011 Linear Algebra and its Applications  
We motivate computations in a multifunctional networked system as instances of algebraic path problems on labeled graphs.  ...  We present an abstract framework, using a special idempotent semiring algebraic path problem, to handle multiple metrics for composition.  ...  Acknowledgements This material is based upon work supported by the MURI Award Agreement W911-NF-0710287 from the Army Research Office and by DARPA under award number 013641-001 for the Multi-Scale Systems  ... 
doi:10.1016/j.laa.2011.02.055 fatcat:rl6dsalm2vfqfbf3lk22wh2ppm

Pattern detection in large temporal graphs using algebraic fingerprints [chapter]

Suhas Thejaswi, Aristides Gionis
2020 Proceedings of the 2020 SIAM International Conference on Data Mining  
In particular, given a vertex-colored temporal graph and a multi-set of colors as a query, we search for temporal paths in the graph that contain the colors specified in the query.  ...  For example, in a real-world graph dataset with more than six million edges and a multi-set query with ten colors, we can extract an optimal solution in less than eight minutes on a haswell desktop with  ...  For the power-law graphs with m = 10 5 edges and multi-set size k = 5, the algebraic algorithm is at least twenty thousand times faster than the baseline.  ... 
doi:10.1137/1.9781611976236.5 dblp:conf/sdm/ThejaswiG20 fatcat:tbljv2j56jb3riym674xncjxlu

Algebraic Traceback Meets Network Coding

Pegah Sattari, Athina Markopoulou
2011 2011 International Symposium on Networking Coding  
In this paper, we consider multi-path graphs that use network coding for marking, and we propose an algebraic traceback scheme that combines marks on packets from different paths for better inference.  ...  So far, algebraic traceback schemes have only been developed to infer single paths, and multipath graphs have been considered as a collection of multiple individual paths [1], [2].  ...  ACKNOWLEDGMENT We would like to thank Christina Fragouli for useful discussion on the duality between problems P1 and P2.  ... 
doi:10.1109/isnetcod.2011.5978944 fatcat:5cmvu3pexvatfgo36v5ywih5m4

Explicit graphs in a functional model for spatial databases

M. Erwig, R.H. Guting
1994 IEEE Transactions on Knowledge and Data Engineering  
We use multi-level order-sorted algebra as a formal framework for the specification of our model.  ...  The classical relational algebra is a universal or one-sorted algebra: it has a single domain whose elements are relations and a collection of functions (such as join) on this domain.  ...  Acknowledgements We would like to thank the referees for their detailed comments and suggestions that helped to improve the paper.  ... 
doi:10.1109/69.317707 fatcat:jkcbi7ygwfeffdvqjlogfqateq

The graded structure of Leavitt Path algebras [article]

R. Hazrat
2011 arXiv   pre-print
Leavitt path algebras associate to directed graphs a Z-graded algebra and in their simplest form recover the Leavitt algebras L(1,k).  ...  In this note, we first study this Z-grading and characterize the ( Z-graded) structure of Leavitt path algebras, associated to finite acyclic graphs, C_n-comet and multi-headed graphs.  ...  In the case of multi-headed weighted rose graphs, a statement similar to Theorem 4.8 can be obtained. For this, we need a weighted version of multi-headed rose graphs. Definition 5.12.  ... 
arXiv:1005.1900v6 fatcat:stndqhnbzbcvhkx6dz5n4q43vq

Connectivity of Dynamic Graphs [chapter]

Michael M. Zavlanos, George J. Pappas
2014 Encyclopedia of Systems and Control  
In this context, graphs have been used widely in the study of robotic and sensor networks and have provided an invaluable modeling framework to address a number of coordinated tasks ranging from exploration  ...  communication has been proven necessary for convergence and performance guarantees. 2  ...  The algebraic connectivity λ 2 (L) and number of paths K k=0 A k metrics can also be combined to give controllers that maintain connectivity, while enforcing desired multi-hop neighborhoods for all agents  ... 
doi:10.1007/978-1-4471-5102-9_213-1 fatcat:wmvxhj4v7ncwldbez5xnflorjq

An algebraic framework for multi-objective and robust variants of path problems

Robert Manger, Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, 10 000 Zagreb, Croatia
2020 Glasnik Matematicki - Serija III  
It is well known that various types of path problems in graphs can be treated together within a common algebraic framework.  ...  A consequence of the obtained algebraic formulation is that multi-objective or robust problem instances can be solved by well-known general algorithms designed to work over an arbitrary path algebra.  ...  The author would like to thank the reviewers for their useful remarks on an earlier version of the paper.  ... 
doi:10.3336/gm.55.1.12 fatcat:grzse3a6zrgibptghjx2tcc7fe

Using graph search algorithms for a rigorous application of emergy algebra rules

A. Marvuglia, B. Rugani, G. Rios, Y. Pigné, E. Benetto, L. Tiruta-Barna
2013 Revue de métallurgie (Imprimé)  
We modeled the Emergy values circulating in multi-component systems with an oriented graph, formalized the problem in a matrix-based structure and developed a variant of the well-known track summing algorithm  ...  This work presents an open source code specifically created for allowing a rigorous Emergy calculation (complying with all the Emergy algebra rules).  ...  An approach based on graph theory has recently been applied to EME by Le Corre and Truffet [20] , where Emergy circulating in a multi-component system is modeled as an oriented graph.  ... 
doi:10.1051/metal/2013050 fatcat:2ml7jiujq5fs5nl2jkkhz53djy

Generalized path-finding algorithms on semirings and the fuzzy shortest path problem

A Boulmakoul
2004 Journal of Computational and Applied Mathematics  
This work starts a safe extension of the path algebra paradigm to valued fuzzy graphs for the shortest path-ÿnding problem.  ...  A new dio d structure k ; ⊕; ⊗; ; e is proposed to solve a path-ÿnding problem in a fuzzy graph. This algebraic structure is adapted precisely to solve the problem of the K-best fuzzy shortest paths.  ...  Klein's algorithm [12] is based on multi-criteria dynamic programming, and can ÿnd a path or paths for a level of membership set by a decision maker.  ... 
doi:10.1016/j.cam.2003.08.027 fatcat:nbuvdwrexjbcfekvrmi5olfpwa

Graph model of the Heisenberg–Weyl algebra

P Blasiak, A Horzela, G H E Duchamp, K A Penson, A I Solomon
2010 Journal of Physics, Conference Series  
It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple interpretation involving, for example, the natural composition of graphs.  ...  We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure.  ...  We further restrict the class of considered graphs to those without cycles, i.e. exclude graphs with closed paths. Example of a multi-vertex graph is shown in fig. 1b .  ... 
doi:10.1088/1742-6596/213/1/012014 fatcat:anl2ifq245fgzg3rx2vxzpss54

An Evidential Path Logic for Multi-Relational Networks [article]

Marko A. Rodriguez, Joe Geldart
2008 arXiv   pre-print
This article presents a non-bivalent, non-monotonic, evidential logic and reasoner that is an algebraic ring over a multi-relational network equipped with two binary operations that can be composed to  ...  Given its multi-relational grounding, it is possible to use the presented evidential framework as another method for structuring knowledge and reasoning in the Semantic Web.  ...  This work was funded by a Director's Fellowship from the Los Alamos National Laboratory, EP-SRC grant EP/D504376/1, and British Telecom plc.  ... 
arXiv:0810.1481v2 fatcat:rjpf7h3jjvc2fjzydkruq7zcdu
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