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### Incremental FO( +, < ) Maintenance of All-Pairs Shortest Paths for Undirected Graphs after Insertions and Deletions [chapter]

Chaoyi Pang, Ramamohanarao Kotagiri, Guozhu Dong
1999 Lecture Notes in Computer Science
We give incremental algorithms, which support both edge insertions and deletions, for the all-pairs shortest-distance problem (APSD) in weighted undirected graphs.  ...  Since FO(+; <) is supported by almost all current database systems, our maintenance algorithms are more appropriate for database applications than non-database query type of maintenance algorithms.  ...  Part of Dong's work was done while visiting Simon Fraser University and George Mason University during his study leave.  ...

### Incremental maintenance of shortest distance and transitive closure in first-order logic and SQL

Chaoyi Pang, Guozhu Dong, Kotagiri Ramamohanarao
2005 ACM Transactions on Database Systems
We give incremental algorithms for (APSD), which support both edge insertions and deletions.  ...  We consider the view maintenance problem for the situation when the database contains a (weighted) graph and the view is either the transitive closure or the answer to the all-pairs shortest-distance problem  ...  Contributions: (1) We give algorithms for incrementally maintaining the all-pairs shortest distance view in graphs after arc insertions and deletions.  ...

### Incremental Graph Computations

Wenfei Fan, Chunming Hu, Chao Tian
2017 Proceedings of the 2017 ACM International Conference on Management of Data - SIGMOD '17
The incremental problem for a class Q of graph queries aims to compute, given a query Q ∈ Q, graph G, output Q(G) and updates ∆G to G as input, changes ∆O to Q(G) such that Q(G⊕∆G) = Q(G)⊕∆O.  ...  No matter how desirable, however, our first results are negative: for common graph queries such as graph traversal, connectivity, keyword search and pattern matching, their incremental problems are unbounded  ...  Algorithm: IncRPQ Input: A graph G with pmarke(·), regular path query Q and NFA M Q , matches Q(G), and batch updates (∆G + , ∆G − ). Output: The updated matches Q(G ⊕ ∆G) and markings pmarke(·).  ...

### Reachability is in DynFO [article]

Samir Datta, Raghav Kulkarni, Anish Mukherjee, Thomas Schwentick, Thomas Zeume
2017 arXiv   pre-print
Patnaik and Immerman introduced the dynamic complexity class DynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions  ...  of edges (Patnaik and Immerman 1997).  ...  The reachability query returns, for a given graph G, all pairs (s, t) of nodes, for which there is a path from s to t.  ...

### Reachability and Distances under Multiple Changes

Samir Datta, Anish Mukherjee, Nils Vortmeier, Thomas Zeume, Michael Wagner
2018 International Colloquium on Automata, Languages and Programming
Recently it was shown that the transitive closure of a directed graph can be updated using firstorder formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework  ...  We show that the former problem can be maintained in DynFO(+, ×) under changes affecting O( log n log log n ) nodes, for graphs with n nodes.  ...  Acknowledgements We thank Rajit Datta and Partha Mukhopadhyay for pointing us to the Agrawal-Vinay technique for computing determinants.  ...

### Practice of Streaming Processing of Dynamic Graphs: Concepts, Models, and Systems [article]

Maciej Besta, Marc Fischer, Vasiliki Kalavri, Michael Kapralov, Torsten Hoefler
2021 arXiv   pre-print
We also crystallize the meaning of different concepts associated with streaming graph processing, such as dynamic, temporal, online, and time-evolving graphs, edge-centric processing, models for the maintenance  ...  of updates, and graph databases.  ...  We thank PRODYNA AG (Darko Križić, Jens Nixdorf, and Christoph K örner) for generous support, and anonymous reviewers for comments that helped to significantly enhance the paper quality.  ...

### Reachability and Distances under Multiple Changes [article]

Samir Datta, Anish Mukherjee, Nils Vortmeier, Thomas Zeume
2018 arXiv   pre-print
Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework  ...  We show that the former problem can be maintained in DynFO(+, ×) under changes affecting O( n/ n) nodes, for graphs with n nodes.  ...  Reachability asks, given a directed graph G, for all pairs s, t of nodes such that there is a path from s to t in G.  ...

### Efficient fully dynamic elimination forests with applications to detecting long paths and cycles [article]

Jiehua Chen, Wojciech Czerwiński, Yann Disser, Andreas Emil Feldmann, Danny Hermelin, Wojciech Nadara, Michał Pilipczuk, Marcin Pilipczuk, Manuel Sorge, Bartłomiej Wróblewski, Anna Zych-Pawlewicz
2020 arXiv   pre-print
We present a data structure that in a dynamic graph of treedepth at most d, which is modified over time by edge insertions and deletions, maintains an optimum-height elimination forest.  ...  More precisely, for a fixed parameter k and a dynamic graph G, modified over time by edge insertions and deletions, our data structures maintain answers to the following queries: - Does G contain a simple  ...  An incremental graph structure is a data structure that maintains an undirected graph G on a xed set of vertices and supports edge insertions.  ...

### Maintenance of 2- and 3-Edge-Connected Components of Graphs II

Han La Poutré
2000 SIAM journal on computing (Print)
., maintenance of transitive closures [16, 17, 18, 27] , minimal spanning trees [7, 8] , planarity testing [3, 4, 6, 25, 33], shortest paths [1, 2, 29], k-connectivity [4, 5, 8, 9, 14, 21, 23, 24, 28,  ...  Data structures and algorithms are presented to efficiently maintain the 2-and 3edge-connected components of a general graph, under insertions of edges and nodes in the graph.  ...  Graphs and terminology. Let G = (V, E) be an undirected graph with V the set of vertices and E the set of edges.  ...

### Maintenance of datalog materialisations revisited

Boris Motik, Yavor Nenov, Robert Piro, Ian Horrocks
2019 Artificial Intelligence
., precompute and store) all facts entailed by a datalog program and a set of explicit facts.  ...  Most such approaches are variants of the counting or Delete/Rederive (DRed) algorithms.  ...  [41] considered all-pairs shortest paths in undirected graphs.  ...

### An Interactive Graph Theory System [chapter]

M. S. Wolfberg
Examples of system use which are presented include finding a shortest path between any pair of vertices in a weighted directed graph, determining the maximally complete subgraphs of an arbitrary graph,  ...  A growing library of these algorithms provides routines to aid in the construction and recognition of various types of graphs. Other routines are used for computing certain properties of graphs.  ...  Examples of system use which are presented include finding a shortest path between any pair of vertices in a weighted directed graph, determining the maximally complete subgraphs of an arbitrary graph,  ...

### Abstracts of Current Computer Literature

1969 IEEE transactions on computers
It has extensive facilities for inserting, deleting, and changing lines of text, a line edit feature, a powerful symbolic search feature, automatic tabs which may be set by the user, and thirty-six buffers  ...  Illustration of Data Management Relations Using Undirected Graphs and Matrices- see 7011.  ...

### An analysis of the graph processing landscape [article]

Miguel E. Coimbra, Alexandre P. Francisco, Luís Veiga
2021 arXiv   pre-print
and different definitions related to the potential for a graph to be updated.  ...  This survey is aimed at both the experienced software engineer or researcher as well as the newcomer looking for an understanding of the landscape of solutions (and their limitations) for graph processing  ...  insertions and bucket deletions.  ...

### 14th International Symposium on Mathematical Programming

1990 Mathematical programming
It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  Finally I report numerical results of a comparison between the variant and a minimization approach using penalty functions.  ...  At each iteration the candidate path P is either extended by adding a new node at the end of the path or contracted by deleting from P the last node inserted, said terminal node.  ...

### Bridging Socially Enhanced Virtual Communities

Venugopal Rao
2013 IOSR Journal of Computer Engineering
For the purpose of bringing the previously separated groups and also finding new relevant groups we introduced broker discovery concept that makes use of techniques and metrics pertaining to interactive  ...  The architecture of the proposed system is compromising of human activities and also automated activities and it is essentially a service oriented system.  ...  Acknowledgement It is our privilege to acknowledge with deep sense of gratitude to our project mentor, Prof.G.G.Chiddarwar for her valuable suggestions and guidance throughout our course of study and timely  ...
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