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- Title
Ranking with submodular functions on a budget.
- Authors
Zhang, Guangyi; Tatti, Nikolaj; Gionis, Aristides
- Abstract
Submodular maximization has been the backbone of many important machine-learning problems, and has applications to viral marketing, diversification, sensor placement, and more. However, the study of maximizing submodular functions has mainly been restricted in the context of selecting a set of items. On the other hand, many real-world applications require a solution that is a ranking over a set of items. The problem of ranking in the context of submodular function maximization has been considered before, but to a much lesser extent than item-selection formulations. In this paper, we explore a novel formulation for ranking items with submodular valuations and budget constraints. We refer to this problem as max-submodular ranking (MSR ). In more detail, given a set of items and a set of non-decreasing submodular functions, where each function is associated with a budget, we aim to find a ranking of the set of items that maximizes the sum of values achieved by all functions under the budget constraints. For the MSR problem with cardinality- and knapsack-type budget constraints we propose practical algorithms with approximation guarantees. In addition, we perform an empirical evaluation, which demonstrates the superior performance of the proposed algorithms against strong baselines.
- Subjects
SUBMODULAR functions; SENSOR placement; APPROXIMATION algorithms; MACHINE learning; VIRAL marketing; BACKPACKS
- Publication
Data Mining & Knowledge Discovery, 2022, Vol 36, Issue 3, p1197
- ISSN
1384-5810
- Publication type
Article
- DOI
10.1007/s10618-022-00833-4