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<Paper uid="W98-1115">
  <Title>Edge-Based Best-First Chart Parsing *</Title>
  <Section position="2" start_page="0" end_page="127" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> Finding one (or all) parses for a sentence according to a context-free grammar requires search.</Paragraph>
    <Paragraph position="1"> Fortunately, there are well known O(n 3) algorithms for parsing, where n is the length of the sentence. Unfortunately, for large grammars (such as the PCFG induced from the Penn II WSJ corpus, which contains around 1.6. i04 rules) and Iongish sentences (say, 40 words and punctuation), even O(n 3) looks pretty bleak.</Paragraph>
    <Paragraph position="2"> One well-known O(n 3) parsing method (Kay, 1980) is chart parsing. In this approach one maintains an agenda of items remaining to be &amp;quot; This material is based on work supported in past by NSF grants IRI-9319516 and SBR-9720368. and by ONR grant N0014-96.- 1-0549.</Paragraph>
    <Paragraph position="3"> processed, one of which is processed during each iteration. As each item is pulled off the agenda, it is added to the chart (unless it is already there, in which case it can be discarded) and used to extend and create additional items. In &amp;quot;exhaustive&amp;quot; chart parsing one removes items from the agenda in some relatively simple way (last-in, first-out is common), and continues to do so until nothing remains.</Paragraph>
    <Paragraph position="4"> A commonly discussed alternative is to remove the constituents from the agenda according to a figure of merit (FOM). The idea is that the FOM selects &amp;quot;good&amp;quot; items to be processed, leaving the ~'bad&amp;quot; ones-- the ones that are not, in fact, part of the correct parse---- sitting on the agenda. When one has a completed parse, or perhaps several possible parses, one simply stops parsing, leaving items remaining on the agenda. The time that would have been spent processing these remaining items is time saved, and thus time earned.</Paragraph>
    <Paragraph position="5"> In our work we have found that exhaustively parsing maximum-40-word sentences from the Penn II treebank requires an average of about 1.2 million edges per sentence. Numbers like this suggest that any approach that offers the possibility of reducing the work load is well worth pursuing, a fact that has been noted by several researchers. Early on, Kay (1980) suggested the use of the chart agenda for this purpose. More recently, the statistical approach to language processing and the use of probabilistic context-free grammars (PCFGs) has suggested using the PCFG probabilities to create a FOM. Bobrow (1990) and Chitrao and Grishman (1990) introduced best-first PCFG parsing, the approach taken here. Subsequent work has suggested different FOMs built from PCFG probabilities (Miller and Fox. 1994: Kochman and Kupin. 1991: Magerman and  Marcus, 1991).</Paragraph>
    <Paragraph position="6"> Probably the most extensive comparison of possible metrics for best-first PCFG parsing is that of Caraballo and Charniak (henceforth C&amp;C) (Forthcoming). They consider a large number of FOMs, and view them as approximations of some &amp;quot;ideal&amp;quot; (but only computable after the fact) FOM. Of these they recommend one as the best of the lot. In this paper we basically adopt both their framework and their recommended FOM. The next section describes their work in more detail, Besides C&amp;C the work that is most directly comparable to ours is that of Goodman (1997) and Ratnaparki (1997). Goodman uses an FOM that is similar to that of C&amp;C but one that should, in general, be somewhat more accurate. However, both Goodman's and Ratnaparki's work assumes that one is doing a beam search of some sort, rather than a best-first search, and their FOM are unfortunately tied to their frameworks and thus cannot be adopted here. We briefly compare our results to theirs in Section 5.</Paragraph>
    <Paragraph position="7"> As noted, our paper takes off from that of C&amp;C and uses the same FOM. The major difference is simply that our parser uses the FOM to rank edges (including incomplete edges), rather than simply completed constituents, as was done by C&amp;C. What is interesting about our approach is that such a seemingly simple change can produce rather dramatic results. Rather than the thousands of edges required by C&amp;C, the parser presented here requires hundreds, or even, if one is willing to pay a small price in accuracy, tens.</Paragraph>
  </Section>
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