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A recent report of Littmann [Commun. ACM '21] outlines the existence and thefatal impact of collusion rings in academic peer reviewing. We introduce andanalyze the problem Cycle-Free Reviewing that aims at finding a reviewassignment without the following kind of collusion ring: A sequence ofreviewers each reviewing a paper authored by the next reviewer in the sequence(with the last reviewer reviewing a paper of the first), thus creating a reviewcycle where each reviewer gives favorable reviews. As a result, all papers inthat cycle have a high chance of acceptance independent of their respectivescientific merit.  We observe that review assignments computed using a standard LinearProgramming approach typically admit many short review cycles. On the negativeside, we show that Cycle-Free Reviewing is NP-hard in various restricted cases(i.e., when every author is qualified to review all papers and one wants toprevent that authors review each other's or their own papers or when everyauthor has only one paper and is only qualified to review few papers). On thepositive side, among others, we show that, in some realistic settings, anassignment without any review cycles of small length always exists. This resultalso gives rise to an efficient heuristic for computing (weighted) cycle-freereview assignments, which we show to be of excellent quality in practice.

Combating Collusion Rings is Hard but Possible