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<Paper uid="P00-1045">
  <Title>Memory-E cient and Thread-Safe Quasi-Destructive Graph Uni cation</Title>
  <Section position="6" start_page="7" end_page="7" type="relat">
    <SectionTitle>
5 Related Work
</SectionTitle>
    <Paragraph position="0"> We reduce memory consumption of graph unication as presented in (Tomabechi, 1991) (or (Wroblewski, 1987)) by separating scratch elds from node structures. Pereira's (Pereira, 1985) algorithm also stores changes to nodes separate from the graph. However, Pereira's mechanism incurs a log(n) overhead for accessing the changes (where n is the number of nodes in a graph), resulting in an O(nlogn) time algorithm. Our algorithm runs in O(n) time.</Paragraph>
    <Paragraph position="1">  by the scratch tables. However, these tables do not consume more than 10 KB in total, and hence have no signi cant impact on the results.</Paragraph>
    <Paragraph position="2"> 7Because the packed version has a variable node size, structure sharing yielded less relative improvements than when applied to the basic version. In terms of number of nodes, though, the two results were identical.</Paragraph>
    <Paragraph position="3"> With respect to over and early copying (as de ned in (Tomabechi, 1991)), our algorithm has the same characteristics as Tomabechi's algorithm. In addition, our algorithm allows to postpone the copying of graphs until after subsumption checks complete. This would require additional elds in the node structure for Tomabechi's algorithm.</Paragraph>
    <Paragraph position="4"> Our algorithm allows sharing of grammar nodes, which is usually impossible in other implementations (Malouf et al., 2000). A weak point of our structure sharing scheme is its extra condition. However, our experiments showed that this condition can have a minor impact on the amount of sharing.</Paragraph>
    <Paragraph position="5"> We showed that compressing node structures allowed us to reduce memory consumption by another 40% without sacri cing performance. Applying the same technique to Tomabechi's algorithm would yield smaller relative improvements (max. 20%), because the scratch elds cannot be compressed to the same extent.</Paragraph>
    <Paragraph position="6"> One of the design goals of Tomabechi's algorithm was to come to an e cient implementation of parallel uni cation (Tomabechi, 1991). Although theoretically parallel unication is hard (Vitter and Simons, 1986), Tomabechi's algorithm provides an elegant solution to achieve limited scale parallelism (Fujioka et al., 1990). Since our algorithm is based on the same principles, it allows parallel uni cation as well. Tomabechi's algorithm, however, is not thread-safe, and hence cannot be used for concurrent uni cation.</Paragraph>
  </Section>
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