Say More Look Up Versus Mashable's Best: E-readers, robovacs, laptops, earbuds, smart home and more Mashable Selects Creator Playbook In My Bag Trending Now Back to School Good Connection: Uplifting stories for a digital age Switch Off Mashable Voices All Series Loop earplugs are actually worth it -- here's how to choose the right pair What you need to know about the earplugs sold during Harry Styles' Madison Square Garden residency. Bethany Allard is a Los Angeles-based shopping reporter at Mashable covering beauty tech, dating, sex and relationships, and headphones. That basically means she puts her hair through a lot, scrolls through a lot of dating apps, and rotates through a lot of different headphones. In addition to testing out and rounding up the best products, she also covers deals for Mashable, paying an especially obsessive amount of attention to Apple deals and prices. That knowledge comes in handy when she's covering shopping holidays like Prime Day and Black Friday, which she's now done for three years at Mashable.

Look Up Switch Off Mashable's Best: E-readers, robovacs, laptops, earbuds, smart home and more Creator Playbook Mashable Voices Trending Now Say More Mashable Selects Safety Net Versus Gift Ideas For Everyone On Your List In My Bag All Series Harry Styles' Loop earplugs are perfect for his Madison Square Garden residency -- where to buy Soumya is a deals writer who covers consumer tech, shopping deals, and the products people use every day. With experience writing about everything from AI tools and software to smartphones and home gadgets, she enjoys breaking down product research into clear, useful recommendations. When she's not tracking deals, she's usually comparing products, digging through reviews, and figuring out what actually makes a purchase worth it. All products featured here are independently selected by our editors and writers. If you buy something through links on our site, Mashable may earn an affiliate commission.

A.1 Proof of Monotonicity and Submodularity In Equation (3a), we stated the objective of the knapsack cover to be Remark 1. f+M is monotonically increasing. A.2 Knapsack Cover To find a solution to problem 3, we use the greedy algorithm proposed by Badanidiyuru and Vondrák [2], which deals with submodular maximization subject to a system of lknapsack constraints and with pmatroid constraints. We present an adapted version of the algorithm in Algorithm 2 where l = 1. Theparameter allows us to 16 trade-off solution time and solution quality. In this work, we set = 0.2.