Utility-Driven Approximate Task Allocation for Crowdsourcing

Abstract

Many applications supported by the crowdsourcing are subject to delay constraints. The timely outcome returned with a better partial fulfillment is preferable to the full completion with delay latency. In this paper, we investigate the approximation algorithms for optimal task assignment with partial fulfillment. The objective is to maximize the total utility gain of all the tasks with delay constraints, where the gain depends on the partial values according to the achievement quality. We propose a linear programming problem with equality constraint, and we prove the objective function value of this problem is an upper bound of that of optimal task assignment. A linear programming based approximate algorithm for task assignment with delay constraints is proposed. The correctness of the algorithm is proved. The approximation ratio is provided. Further the problem of optimal task assignment with relaxed constrains is proposed and a lagrange multiplier based approximation algorithm with $O \left( {\mathop {\max }\nolimits_{i \in \{ 1,...,n\} } \{ {r_i}\} n } \right)$ is given. Evaluation results show that our algorithms have better performance in utility gain.