[comp.theory] It SOUNDS simple enough ?!?! ...

harrison@ENUXHA.EAS.ASU.EDU (John V. Harrison) (02/20/91)

Greetings to all great scholars, near and far!!!!!
Please take a moment to consider the following (simple?) problem.

Given:

Consider a directed graph and its transitive closure.  Let the graph be 
represented by a boolean adjacency (incidence) matrix A. Let the transitive 
closure be represented be a boolean (reachability) matrix TC. 

(Simple?) Problem:

How can TC be updated (without completely recomputing TC) when an edge of the 
graph is deleted (i.e. an element in A is set to 0)?  Is there a better 
representation than a matrix for the dynamic graph and its transitive closure 
that can support the fast update of the transitive closure when an edge is 
deleted (or perhaps require less space)?  Surely this problem has been 
encountered! 

I would appreciate it if someone could suggest a solution or
point me towards some relevant literature.

Thanks, 
John         

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John Harrison                           harrison@enuxha.eas.asu.edu
Department of Computer Science
Arizona State University
Tempe, AZ  85287