We consider the problem of maximizing the sum of a monotone submodular function and a linear function subject to a general solvable polytope constraint. Recently, Sviridenko et al.  described an algorithm for this problem whose approximation guarantee is optimal in some intuitive and formal senses. Unfortunately, this algorithm involves a guessing step which makes it less clean and significantly affects its time complexity. In this work we describe a clean alternative algorithm that uses a novel weighting technique in order to avoid the problematic guessing step while keeping the same approximation guarantee as the algorithm of .
|Title of host publication||Algorithms and Data Structures - 16th International Symposium, WADS 2019, Proceedings|
|Editors||Zachary Friggstad, Mohammad R. Salavatipour, Jörg-Rüdiger Sack|
|Number of pages||15|
|State||Published - 2019|
|Event||16th International Symposium on Algorithms and Data Structures, WADS 2019 - Edmonton, Canada|
Duration: 5 Aug 2019 → 7 Aug 2019
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||16th International Symposium on Algorithms and Data Structures, WADS 2019|
|Period||5/08/19 → 7/08/19|
Bibliographical noteFunding Information:
by Israel Science Foundation grant
This research was partially supported by Israel Science Foundation grant number 1357/16.
© Springer Nature Switzerland AG 2019.
- Continuous greedy
- Submodular maximization