A Generalization of the AL method for Fair Allocation of Indivisible Objects

We consider the assignment problem in which agents express ordinal preferences over $m$ objects and the objects are allocated to the agents based on the preferences. In a recent paper, Brams, Kilgour, and Klamler (2014) presented the AL method to compute an envy-free assignment for two agents. The AL method crucially depends on the assumption that agents have strict preferences over objects. We generalize the AL method to the case where agents may express indifferences and prove the axiomatic properties satisfied by the algorithm. As a result of the generalization, we also get a $O(m)$ speedup on previous algorithms to check whether a complete envy-free assignment exists or not. Finally, we show that unless P=NP, there can be no polynomial-time extension of GAL to the case of arbitrary number of agents

Spartan Daily, September 6, 1996

Volume 107, Issue 6https://scholarworks.sjsu.edu/spartandaily/8862/thumbnail.jp

Spartan Daily, November 14, 1972

Volume 60, Issue 36https://scholarworks.sjsu.edu/spartandaily/5671/thumbnail.jp

Santa Fe Daily New Mexican, 04-06-1896

https://digitalrepository.unm.edu/sfnm_news/6279/thumbnail.jp

Optical NP problem solver on laser-written waveguide platform

Cognitive photonic networks are researched to efficiently solve computationally hard problems. Flexible fabrication techniques for the implementation of such networks into compact and scalable chips are desirable for the study of new optical computing schemes and algorithm optimization. Here we demonstrate a femtosecond laser-written optical oracle based on cascaded directional couplers in glass, for the solution of the Hamiltonian path problem. By interrogating the integrated photonic chip with ultrashort laser pulses, we were able to distinguish the different paths traveled by light pulses, and thus infer the existence or the absence of the Hamiltonian path in the network by using an optical correlator. This work proves that graph theory problems may be easily implemented in integrated photonic networks, down scaling the net size and speeding up execution times

Vol. 34, No. 16, February 12, 1986

•Committee Scraps Proposed Flyback Break Idea •lglitzin Acquitted of Trespass •Indian Expert Visiting School for Semester •Prof. Allen to Retire at Year-end •Say No to Sub-one Computers •Don\u27t Bank on it •Religion not Trivialized by Separation of Church and State •Odle Analyzes First Year Experience •New Senate Election Procedure Narrowly Defeated •More Sandalow: the University Owns the Library •Notices •The Color Gold, Not Always What It Appears •Crossword •Law in the Raw •Grade Expectations: Our \u27Bleak House\u2

Western Liberal, 04-18-1913

https://digitalrepository.unm.edu/lwl_news/1766/thumbnail.jp