Programming Assignment 6: WordNet

WordNet is a semantic lexicon for the English language that computational linguists and cognitive scientists use extensively. For example, WordNet was a key component in IBM's Jeopardy-playing Watson computer system. WordNet groups words into sets of synonyms called synsets. For example, { AND circuit, AND gate } is a synset that represent a logical gate that fires only when all of its inputs fire. WordNet also describes semantic relationships between synsets. One such relationship is the is-a relationship, which connects a hyponym (more specific synset) to a hypernym (more general synset). For example, the synset { gate, logic gate } is a hypernym of { AND circuit, AND gate } because an AND gate is a kind of logic gate.

The WordNet digraph. Your first task is to build the WordNet digraph: each vertex v is an integer that represents a synset, and each directed edge v→w represents that w is a hypernym of v. The WordNet digraph is a rooted DAG: it is acyclic and has one vertex—the root—that is an ancestor of every other vertex. However, it is not necessarily a tree because a synset can have more than one hypernym. A small subgraph of the WordNet digraph appears below.

The WordNet input file formats. We now describe the two data files that you will use to create the WordNet digraph. The files are in comma-separated values (CSV) format: each line contains a sequence of fields, separated by commas.

WordNet data type. Implement an immutable data type WordNet with the following API:

public class WordNet {

   // constructor takes the name of the two input files
   public WordNet(String synsets, String hypernyms)

   // all WordNet nouns
   public Iterable<String> nouns()

   // is the word a WordNet noun?
   public boolean isNoun(String word)

   // a synset (second field of synsets.txt) that is a shortest common ancestor
   // of noun1 and noun2 (defined below)
   public String sca(String noun1, String noun2)

   // distance between noun1 and noun2 (defined below)
   public int distance(String noun1, String noun2)

   // do unit testing of this class
   public static void main(String[] args)
}
Corner cases.  All methods and the constructor should throw a java.lang.NullPointerException if any argument is null. The distance() and sca() methods should throw a java.lang.IllegalArgumentException unless both of the noun arguments are WordNet nouns. You may assume that the input files are in the specified format (and that the underlying digraph is a rooted DAG).

Performance requirements.  Your data type should use space linear in the input size (size of synsets and hypernyms files). The constructor should take time linearithmic (or better) in the input size. The method isNoun() should run in time logarithmic (or better) in the number of nouns. The methods distance() and sca() should make exactly one call to the length() and ancestor() methods in ShortestCommonAncestor, respectively. For the analysis, assume that the number of characters in a noun or synset is bounded by a constant.

Shortest common ancestor. An ancestral path between two vertices v and w in a rooted DAG is a directed path from v to a common ancestor x, together with a directed path from w to the same ancestor x. A shortest ancestral path is an ancestral path of minimum total length. We refer to the common ancestor in a shortest ancestral path as a shortest common ancestor. Note that a shortest common ancestor always exists because the root is an ancestor of every vertex. Note also that an ancestral path is a path, but not a directed path.

We generalize the notion of shortest common ancestor to subsets of vertices. A shortest ancestral path of two subsets of vertices A and B is a shortest ancestral path over all pairs of vertices v and w, with v in A and w in B. The figure below shows an example in which, for two subsets, red and blue, we have computed several (but not all) ancestral paths, including the shortest one.


Shortest common ancestor data type. Implement an immutable data type ShortestCommonAncestor with the following API:

public class ShortestCommonAncestor {

   // constructor takes a rooted DAG as argument
   public ShortestCommonAncestor(Digraph G)

   // length of shortest ancestral path between v and w
   public int length(int v, int w)

   // a shortest common ancestor of vertices v and w
   public int ancestor(int v, int w)

   // length of shortest ancestral path of vertex subsets A and B
   public int length(Iterable<Integer> subsetA, Iterable<Integer> subsetB)

   // a shortest common ancestor of vertex subsets A and B
   public int ancestor(Iterable<Integer> subsetA, Iterable<Integer> subsetB)

   // do unit testing of this class
   public static void main(String[] args)
}

Corner cases.  All methods and the constructor should throw a java.lang.NullPointerException if any argument is null or if any iterable argument contains a null item. The constructor should throw a java.lang.IllegalArgumentException if the digraph is not a rooted DAG. The methods length() and ancestor() should throw a java.lang.IndexOutOfBoundsException if any argument vertex is invalid and a java.lang.IllegalArgumentException if any iterable argument contains zero vertices.

Basic performance requirements.  Your data type should use space proportional to E + V, where E and V are the number of edges and vertices in the digraph, respectively. All methods and the constructor should take time proportional to E + V (or better).

Additional performance requirements.  For extra credit, in addition, the methods length() and ancestor() should take time proportional to the number of vertices and edges reachable from the argument vertices (or better), For example, to compute the shortest common ancestor of v and w in the digraph below, your algorithm can examine only the highlighted vertices and edges and it cannot initialize any vertex-indexed arrays.

Test client. The following test client takes the name of a digraph input file as as a command-line argument, creates the digraph, reads in vertex pairs from standard input, and prints the length of the shortest ancestral path between the two vertices along with a shortest common ancestor:

public static void main(String[] args) {
    In in = new In(args[0]);
    Digraph G = new Digraph(in);
    ShortestCommonAncestor sca = new ShortestCommonAncestor(G);
    while (!StdIn.isEmpty()) {
        int v = StdIn.readInt();
        int w = StdIn.readInt();
        int length   = sca.length(v, w);
        int ancestor = sca.ancestor(v, w);
        StdOut.printf("length = %d, ancestor = %d\n", length, ancestor);
    }
}
Here is a sample execution (the bold indicates what you type):
% more digraph1.txt             % java-algs4 ShortestCommonAncestor digraph1.txt
12                              3 10
11                              length = 4, ancestor = 1
 6  3                            
 7  3                           8 11
 3  1                           length = 3, ancestor = 5
 4  1
 5  1                           6 2
 8  5                           length = 4, ancestor = 0
 9  5
10  9
11  9
 1  0
 2  0

Measuring the semantic relatedness of two nouns. Semantic relatedness refers to the degree to which two concepts are related. Measuring semantic relatedness is a challenging problem. For example, you consider George W. Bush and John F. Kennedy (two U.S. presidents) to be more closely related than George W. Bush and chimpanzee (two primates). It might not be clear whether George W. Bush and Eric Arthur Blair are more related than two arbitrary people. However, both George W. Bush and Eric Arthur Blair (aka George Orwell) are famous communicators and, therefore, closely related.

We define the semantic relatedness of two WordNet nouns x and y as follows:

This is the notion of distance that you will use to implement the distance() and sca() methods in the WordNet data type.

Outcast detection. Given a list of WordNet nouns x1, x2, ..., xn, which noun is the least related to the others? To identify an outcast, compute the sum of the distances between each noun and every other one:

di   =   distance(xi, x1)   +   distance(xi, x2)   +   ...   +   distance(xi, xn)
and return a noun xt for which dt is maximum. Note that because distance(xi, xi) = 0, it will not contribute to the sum.

Implement an immutable data type Outcast with the following API:

public class Outcast {
   public Outcast(WordNet wordnet)         // constructor takes a WordNet object
   public String outcast(String[] nouns)   // given an array of WordNet nouns, return an outcast
   public static void main(String[] args)  // see test client below
}
Assume that argument to outcast() contains only valid WordNet nouns (and that it contains at least two such nouns).

The following test client takes from the command line the name of a synset file, the name of a hypernym file, followed by the names of outcast files, and prints out an outcast in each file:

public static void main(String[] args) {
    WordNet wordnet = new WordNet(args[0], args[1]);
    Outcast outcast = new Outcast(wordnet);
    for (int t = 2; t < args.length; t++) {
        In in = new In(args[t]);
        String[] nouns = in.readAllStrings();
        StdOut.println(args[t] + ": " + outcast.outcast(nouns));
    }
}
Here is a sample execution:
% more outcast5.txt
horse zebra cat bear table

% more outcast8.txt
water soda bed orange_juice milk apple_juice tea coffee

% more outcast11.txt
apple pear peach banana lime lemon blueberry strawberry mango watermelon potato


% java-algs4 Outcast synsets.txt hypernyms.txt outcast5.txt outcast8.txt outcast11.txt
outcast5.txt: table
outcast8.txt: bed
outcast11.txt: potato

Analysis of running time. Analyze the potential effectiveness of your approach to this problem by answering the questions below:

Your answers should be given as a function of the number of vertices V and the number of edges E in the digraph.

Deliverables. Submit WordNet.java, ShortestCommonAncestor.java, and Outcast.java that implement the APIs described above, along with a readme.txt file. Also submit any other supporting files (excluding those in algs4.jar). You may not call any library functions other than those in java.lang, java.util, and algs4.jar.



This assignment was created by Alina Ene and Kevin Wayne.
Copyright © 2006