Suppose you ran a chess tournament, everybody played everybody, and you wanted to use the results to rank everybody. Unless you were really lucky, the results would not be acyclic...
Consider the system of Diophantine equations x2 − ay2 = b, P (x, y) = z2, where P is a given integer polynomial. Historically, such systems have been analyzed by using Baker’s ...
We give new algorithms for a variety of randomly-generated instances of computational problems using a linearization technique that reduces to solving a system of linear equations...
In multiagent settings where agents have different preferences, preference aggregation can be an important issue. Voting is a general method to aggregate preferences. We consider ...
Attempts at classifying computational problems as polynomial time solvable, NP-complete, or belonging to a higher level in the polynomial hierarchy, face the difficulty of undecid...