Current Trends in Fair Division and Scheduling Algorithms
Recent research in the fields of fair division and scheduling algorithms has seen significant advancements, particularly in the areas of randomized algorithms for fair allocation, heuristic approaches to scheduling problems, and novel constraint programming models for batch scheduling. The focus has been on enhancing the efficiency and fairness of these algorithms, often through the introduction of new concepts such as ex-ante proportionality in randomized allocation methods and the development of more synchronized constraint programming models for batch scheduling. Additionally, there has been a notable push towards ensuring fairness in allocation problems with mixed manna and unequal entitlements, as well as in facility location games, where the analysis of incentives and fairness in ordered weighted average methods has provided deeper insights into mechanism design.
Noteworthy Developments
- Randomized Envy-Cycle-Elimination Algorithm: Demonstrates potential for ex-ante proportionality in fair allocation problems, though challenges remain for more than two agents.
- Simulated Annealing in Scheduling: Proves effective in achieving near-optimal solutions for identical parallel machine scheduling problems, offering a viable heuristic alternative to exact methods.
- Redundant Synchronized Model: Introduces a novel approach to batch scheduling with incompatible job families, significantly improving solution optimality and speed.
- Mixed Manna Allocation with Unequal Entitlements: Advances the understanding of fair division by proposing a polynomial-time algorithm for weighted envy-freeness up to 1 transfer.
