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Low-Memory Tour Reversal in Directed Graphs

Authors Viktor Mosenkis, Uwe Naumann, Elmar Peise



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Viktor Mosenkis
Uwe Naumann
Elmar Peise

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Viktor Mosenkis, Uwe Naumann, and Elmar Peise. Low-Memory Tour Reversal in Directed Graphs. In Combinatorial Scientific Computing. Dagstuhl Seminar Proceedings, Volume 9061, pp. 1-3, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.09061.12

Abstract

We consider the problem of reversing a {em tour} $(i_1,i_2,ldots,i_l)$ in a directed graph $G=(V,E)$ with positive integer vertices $V$ and edges $E subseteq V imes V$, where $i_j in V$ and $(i_j,i_{j+1}) in E$ for all $j=1,ldots,l-1.$ The tour can be processed in last-in-first-out order as long as the size of the corresponding stack does not exceed the available memory. This constraint is violated in most cases when considering control-flow graphs of large-scale numerical simulation programs. The tour reversal problem also arises in adjoint programs used, for example, in the context of derivative-based nonlinear optimization, sensitivity analysis, or other, often inverse, problems. The intention is to compress the tour in order not to run out of memory. As the general optimal compression problem was proven to be NP-hard and big control-flow graphs results from loops in programs we do not want to use general purpose algorithms to compress the tour. We want rather to compress the tour by finding loops and replace the redundant information by proper representation of the loops.
Keywords
  • Directed graph
  • tour reversal
  • offline algorithm
  • dynamic programming
  • online algorithm
  • control-flow reversal
  • adjoint program

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