Graph modeling
You are required to provide solutions for the following problems using a graph formulation of the
setting of the problem, a graph algorithm that solves the problem and a run time analysis of the
algorithm in terms of the size of the graph nodes and edges.
In graph formulation, you need to specify the following.
(A.) An example diagram illustrating the graph.
(B.) What the nodes $V$ of the graph $G$ are.
(C.) What the edges $E \subseteq V \times V$ of the graph $G$ are.
(D.) In case the graph has weights, what the weights $W$ are
• And how the edges map to them $w: E \mapsto W$.
Notice that multiple correct solutions exist for each of the problems. So do not hesitate to be
creative.
Problem 5: Language dictionaries (25 pts.)
Consider a set of languages and a set of dictionaries that return synonyms of a word in its own
language, or translation of the word in other languages. We are interested in checking whether two
words $w_1$ in language $l_1$ and $w_2$ in language $l_2$ are related semantically. We are also interested in
checking whether a pairs of words ($w_1, w_2$) is more related than another pair of words ($u_1, u_2$).
Formulate both problems as graph problems and provide solutions for them.
Graph formulation is worth (10 pts.), correct algorithms are worth (10 pts.) and the runtime
analysis is worth (5 pts.).
