Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: The assignment of unique IDs to n variables is an instance of the well-known renaming problem, for which multiple algorithms have been proposed in the literature on distributed algorithms. However, to our knowledge, all these algorithms focus on robustness to failures, and ignore the issue of privacy. On the contrary, in this paper we do not consider agent failures, and we rather need an algorithm that protects agent and topology privacy. To this purpose, we propose Algorithm 1, which is a modification of the pseudo-tree generation algorithm in Online Appendix 2, and is an improved version of the algorithm proposed by Léauté and Faltings (2009). Each variable x is assigned a unique number idx that corresponds to the order in which it is first visited during the distributed traversal of the constraint graph (or, more precisely, an upper bound thereon). This is done by appending to each CHILD message the number id of variables visited so far (lines 8, 29 and 31). Each variable adds a random number to id so as not to leak any useful upper bound on its number of neighbors (lines 5 and 15). At the end of this algorithm, the root variable discovers an upper bound n+ on the total number of variables, and reveals it to everyone (lines 35 and 22 to 24).

Protecting Privacy through Distributed Computation in Multi-agent Decision Making Online Appendix 3: Unique ID Generation Algorithm