Computing Approximate Pareto Frontiers for Submodular Utility and Cost Tradeoffs
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arXiv
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| Format: | Preprint |
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2026
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| author | Vombatkere, Karan Terzi, Evimaria |
| author_facet | Vombatkere, Karan Terzi, Evimaria |
| contents | In many data-mining applications, including recommender systems, influence maximization, and team formation, the goal is to pick a subset of elements (e.g., items, nodes in a network, experts to perform a task) to maximize a monotone submodular utility function while simultaneously minimizing a cost function. Classical formulations model this tradeoff via cardinality or knapsack constraints, or by combining utility and cost into a single weighted objective. However, such approaches require committing to a specific tradeoff in advance and return only a single solution, offering limited insight into the space of viable utility-cost tradeoffs. In this paper, we depart from the single-solution paradigm and examine the problem of computing representative sets of high-quality solutions that expose different tradeoffs between submodular utility and cost. For this, we introduce $(α_1,α_2)$-approximate Pareto frontiers that provably approximate the achievable tradeoffs between submodular utility and cost. Specifically, we formalize the Pareto-$\langle f,c \rangle$ problem and develop efficient algorithms for multiple instantiations arising from different combinations of submodular utility $f$ and cost functions $c$. Our results offer a principled and practical framework for understanding and exploiting utility-cost tradeoffs in submodular optimization. Experiments on datasets from diverse application domains demonstrate that our algorithms efficiently compute approximate Pareto frontiers in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15964 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing Approximate Pareto Frontiers for Submodular Utility and Cost Tradeoffs Vombatkere, Karan Terzi, Evimaria Data Structures and Algorithms Discrete Mathematics Social and Information Networks In many data-mining applications, including recommender systems, influence maximization, and team formation, the goal is to pick a subset of elements (e.g., items, nodes in a network, experts to perform a task) to maximize a monotone submodular utility function while simultaneously minimizing a cost function. Classical formulations model this tradeoff via cardinality or knapsack constraints, or by combining utility and cost into a single weighted objective. However, such approaches require committing to a specific tradeoff in advance and return only a single solution, offering limited insight into the space of viable utility-cost tradeoffs. In this paper, we depart from the single-solution paradigm and examine the problem of computing representative sets of high-quality solutions that expose different tradeoffs between submodular utility and cost. For this, we introduce $(α_1,α_2)$-approximate Pareto frontiers that provably approximate the achievable tradeoffs between submodular utility and cost. Specifically, we formalize the Pareto-$\langle f,c \rangle$ problem and develop efficient algorithms for multiple instantiations arising from different combinations of submodular utility $f$ and cost functions $c$. Our results offer a principled and practical framework for understanding and exploiting utility-cost tradeoffs in submodular optimization. Experiments on datasets from diverse application domains demonstrate that our algorithms efficiently compute approximate Pareto frontiers in practice. |
| title | Computing Approximate Pareto Frontiers for Submodular Utility and Cost Tradeoffs |
| topic | Data Structures and Algorithms Discrete Mathematics Social and Information Networks |
| url | https://arxiv.org/abs/2602.15964 |