Parallel Greedy Approximation on Large-Scale Combinatorial Auctions

Abstract

Combinatorial auctions (Cramton et al., 2006) are auctions that allow bidders to place bids for a set of items. Combinatorial auctions provide suitable mechanisms for efficient allocation of resources to self-interested attendees (Cramton et al., 2006). Therefore, many works have been done to utilize combinatorial auction mechanisms for efficient resource allocation. For example, the FCC tried to employ combinatorial auction mechanisms for assigning spectrums to companies (McMillan, 1994). On the other hand, efficient resource allocation is also becoming crucial in many computer systems that should manage resources efficiently, and combinatorial auction mechanisms are suitable for this situation. For example, considering a ubiquitous computing scenario, there is typically a limited amount of resources (sensors, devices, etc.) that may not cover all needs for all users. Due to certain reasons (physical limitations, privacy, etc.), most of the resources cannot be shared with other users. Furthermore, software agents will use two or more resources at a time to achieve desirable services for users. Of course, each software agent provides services to its own user, and the agent may be self-interested. Tremendous research efforts have been done to improve many parts of combinatorial auctions. An example is recent efforts for winner determination problem. In general, the optimal winner determination problem of a combinatorial auction is NP-hard (Cramton et al., 2006) for the number of bids. Thus, much work focuses on tackling the computational costs for winner determination (Fujishima et al., 1999); (Cramton et al., 2006); (Sandholm et al., 2005). Also many efforts have been done for generic problem solvers that can be applied to solve winner determination problems. However, in such ubiquitous computing scenarios, there is strong demand for completing an auction within a fine-grained time period without loss of allocation efficiency. In a ubiquitous computing scenario, the physical location of users may always be changing and that could be handled by the system. Also, each user may have multiple goals with different contexts, and those contexts are also dynamically changing. Therefore, resources should be re-allocated in a certain fine-grained period to keep up with those changes in a timely manner. For better usability, the time period of resource reallocation will be 0.1 to several