Simultaneous approximations for adversarial and stochastic online budgeted allocation

Motivated by online ad allocation, we study the problem of simultaneous approximations for the adversarial and stochastic online budgeted allocation problem. This problem consists of a bipartite graph G = (X, Y, E), where the nodes of Y along with their corresponding capacities are known beforehand to the algorithm, and the nodes of X arrive online. When a node of X arrives, its incident edges, and their respective weights are revealed, and the algorithm can match it to a neighbor in Y . The objective is to maximize the weight of the final matching, while respecting the capacities. When nodes arrive in an adversarial order, the best competitive ratio is known to be 1 − 1/e, and it can be achieved by the Ranking [18], and its generalizations (Balance [16, 21]). On the other hand, if the nodes arrive through a random permutation, it is possible to achieve a competitive ratio of 1 − [9]. In this paper we design algorithms that achieve a competitive ratio better than 1 − 1/e on ave...

• Type: Journal
• Year: 2012
• Where: SODA
• Authors: Vahab S. Mirrokni, Shayan Oveis Gharan, Morteza Zadimoghaddam
• Keywords: Algorithms, Approximation Factor, Random Permutation, SODA 2012, Unweighted Graphs