Abstract
In this paper, we introduce a new problem which we call as Online Probabilistic Weighted Bipartite Graph Matching. Consider a weighted bipartite graph with a source node set, a target node set, an edge set and a set of weights for the edges. The source nodes arrive in an online fashion based on a stochastic process. When a source node arrives, it needs to be matched with a target node before the arrival of next source node. Since the arrival process is stochastic, all the source nodes need not arrive and their order of arrival is also not known a priori. The objective is to match the arriving source node with a target node such that the expected sum of weights of the matching over the arrival process is maximized. We present some heuristics that perform well for this problem. We demonstrate the application of our formulation for session based recommendation [5]. Here the source nodes correspond to the web pages, the target nodes correspond to the advertisement that can be shown and the edge weights correspond to the revenue generated by showing the given advertisement on the given web page. The user traversal of web pages corresponds to the arrival process of the source nodes.
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Modani, N., Sabharwal, Y., Karthik, S. (2005). A Framework for Session Based Recommendations. In: Bauknecht, K., Pröll, B., Werthner, H. (eds) E-Commerce and Web Technologies. EC-Web 2005. Lecture Notes in Computer Science, vol 3590. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11545163_11
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DOI: https://doi.org/10.1007/11545163_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28467-3
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