Some friends of yours maintain a popular news and discussion site on the Web, and the traffic has reached a level where they want to begin differentiating their visitors into paying and nonpaying customers. A standard way to do this is to make all the content on the site available to customers who pay a monthly subscription fee; meanwhile, visitors who don t subscribe can still view a subset of the pages (all the while being bombarded with ads asking them to become subscribers).
Here are two simple ways to control access for nonsubscribers: You could (1) designate a fixed subset of pages as viewable by nonsubscribers, or (2) allow any page in principle to be viewable, but specify a maximum number of pages that canbe viewed by a nonsubscriber in a single session. (We ll assume the site is able to track the path followed by a visitor through the site.)
Your friends are experimenting with a way of restricting access that is different from and more subtle than either of these two options. They want nonsubscribers to be able to sample different sections of the Web site, so they designate certain subsets of the pages as constituting particular zones–for example, there can be a zone for pages on politics, a zone for pages on music, and so forth. It s possible for a page to belong to more than one zone. Now, as a nonsubscribing user passes through the site, the access policy allows him or her to visit one page from each zone, but an attempt by the user to access a second page from the same zone later in the browsing session will be disallowed. (Instead, the user will be directed to an ad suggesting that he or she become a subscriber.)
More formally, we can model the site as a directed graph G = (V, E),in which the nodes represent Web pages and the edges represent directed hyperlinks. There is a distinguished entry node s ε V, and there are zones Z1,…,Zk ⊆ V. A path P taken by a nonsubscriber is restricted to include at most one node from each zone Zi.
One issue with this more complicated access policy is that it gets difficult to answer even basic questions about reachability, including: Is it possible for a nonsubscriber to visit a given node t? More precisely, we define the Evasive Path Problem as follows: Given G, Z1,…, Zk, s e V, and a destination node t ε V, is there an s-t path in G that includes at most one node from each zone Zi? Prove that Evasive Path is NP-complete.
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