Daily Times

LAHORE: Haris Aziz, an alumnus of the Lahore University of Management Sciences (LUMS), has come up with a solution to a problem that has been plaguing scientists for years; how to allocate resources fairly to any number of people so that each is left satisfied with his/her share.

Dividing a thing in two fairly is easy enough, but when there are more people involved is when the task becomes more difficult. In the 20th century, John Selfridge and John Conway independently developed a solution for envy-free cake cutting for three people.

Aziz said he first started working, along with his co-author Simon Mackenzie, on the solution some 18 months ago. He said the problem for four or more persons was unresolved for years. “We first came up with an algorithm for the case of four persons.”

He said that the paper, titled, A Discrete and Bounded Envy-Free Cake Cutting Protocol for Any Number of Agents, had been accepted at STOC (a prominent theoretical computer science conference) and will be presented in Boston this June.

Their solution has been described as a “major breakthrough” by Professor Steven Brams at New York University, who has worked on such problems for more than 20 years. Although the paper is yet to be peer reviewed, Professor Brams told the Sydney Morning Herald the “results look solid”.

However, he also said that the Aziz-Mackenzie protocol is too complex for practical application and Aziz agrees with him. “Not only is the algorithm complex but the number of steps it takes to get the job done can be too high in the worst case. So our result should be viewed as a mathematical result rather than a practical engineering result.”