An analysis of approximations for maximizing submodular set functions—I
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Submodular maximization (from the classical greedy analysis of Nemhauser-Wolsey-Fisher [12]) underpins cache and content placement [20]; the matroid-constrained guarantees we invoke are due to Fisher-Nemhauser-Wolsey [54] (combinatorial greedy, 1/2), Calinescu-Chekuri-Pál-Vondrák [53] (continuous greedy, 1-1/e), and, for the matroid-plus-knapsack case, Lee-Mirrokni-Nagarajan-Sviridenko [62] (local
“Submodular maximization (from the classical greedy analysis of Nemhauser-Wolsey-Fisher [12]) underpins cache and content placement [20]; the matroid-constrained guarantees we invoke are due to Fisher-Nemhauser-Wolsey [54] (combinatorial greedy, 1 2 ), Calinescu-Chekuri-Pál-Vondrák [53] (continuous greedy, 1 -1 /e ), and, for the matroid-plus-knapsack case, Lee-Mirrokni-Nagarajan-Sviridenko [62] (”
From Janus: Joint Prefill/Decode Disaggregation with KV-Cache-Aware Multi-Cloud Routing for Edge-Adjacent LLM Serving (2026) · cites this paper as [12]
Our drift-plus-penalty machinery is classical [13]; the contribution is composing it with submodular prefix placement [12, 53, 54], a combination we have not seen analyzed.
“Our drift-pluspenalty machinery is classical [13]; the contribution is composing it with submodular prefix placement [12, 53, 54], a combination we have not seen analyzed.”
From Janus: Joint Prefill/Decode Disaggregation with KV-Cache-Aware Multi-Cloud Routing for Edge-Adjacent LLM Serving (2026) · cites this paper as [12]
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References 16 · Cited by 4,412
- Authors
- Nemhauser, G. L., Wolsey, L. A., & Fisher, M. L.
- Affiliations
- UCLouvain (BE)
- University of Pennsylvania (US)
- Venue
- Mathematical Programming
- Published
- 1978-12
- Volume
- 14
- Issue
- 1
- Pages
- 265-294
- ISSN
- 0025-5610 (ISSN-L)
- 1436-4646
- OpenAlex
- W1680189815
- Cited by
- 4,412
- References
- 16
- Citations by year
- 2026: 231 · 2025: 201 · 2024: 194 · 2023: 258 · 2022: 266 · 2021: 354 · 2020: 346 · 2019: 323 · 2018: 318 · 2017: 287 · 2016: 279 · 2015: 273 · 2014: 243 · 2013: 179 · 2012: 159
- FWCI
- 10.51
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Mathematical Programming (publishedVersion)
- Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Complexity and Algorithms in Graphs
- Physical Sciences › Computer Science › Computer Networks and Communications › Optimization and Search Problems
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Keywords
- submodular functions, approximation algorithms, combinatorial optimization, matroid optimization, maximum weight independent set, greedy algorithm, linear programming relaxation
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