Ranking an Assortment of Products via Sequential Submodular Optimization

We study an optimization problem capturing a core operational question for online retailing platforms. Given models for the users' preferences over products as well as the number of items they are willing to observe before clicking on one or abandoning the search, what is the best way to rank the relevant products in response to a search query? In order to capture both popularity and diversity effects, we model the probability that a user clicks on an element from a subset of products as a monotone submodular function of this set. We also assume that the patience level of the users, or the number of items they are willing to observe before clicking on one or abandoning the search, is a given random variable. Under those assumptions, the objective functions capturing user engagement or platform revenue can be written as a new family of submodular optimization problems over a sequence of elements. We call this family of natural optimization problems sequential submodular optimization. By building on and extending the literature on submodular maximization subject to matroid constraints, we derive a (1-1/e) optimal approximation algorithm for maximizing user engagement and a bi-criteria approximation algorithm for maximizing revenue subject to a lower bound on user engagement

An O(log n/log log n)-approximation algorithm for the asymmetric traveling salesman problem

URL to paper on conference siteWe consider the Asymmetric Traveling Salesman problem for costs satisfying the triangle inequality. We derive a randomized algorithm which delivers a solution within a factor O(log n/ log log n) of the optimum with high probability.National Science Foundation (U.S.) (Fulbright Science and Technology Award, contract CCF- 0829878)National Science Foundation (U.S.) (contract CCF- 0829878)United States. Office of Naval Research (ONR grant N00014-05-1-0148

An approximation algorithm for max-min fair allocation of indivisible goods

In this paper we give the first approximation algorithm for the problem of max-min fair allocation of indivisible goods. 1 The approximation ratio of our algorithm is Ω ( √ k log3). As k a part of our algorithm, we design an iterative method for rounding a fractional matching on a tree which might be of independent interest

An approximation algorithm for max-min fair allocation of indivisible goods

In this paper, we give the first approximation algorithm for the problem of max-min fair 1 allocation of indivisible goods. The approximation ratio of our algorithm is √ k log3. As k a part of our algorithm, we design an iterative method for rounding a fractional matching on a tree which might be of independent interest

Cucurbita maxima (Pumpkin) seeds: Scolicidal activity and preventive efficacy of its extract on experimental hydatidosis in mice

Introduction: Hydatid Disease (HD), a helminth infection with various clinical complications is a serious economic and public health concern around the world. Nowadays, different agents have been broadly applied as scolicids; these agents have several side effects on patients. Therefore, the aims of this experimental study were to evaluate the scolicidal activity of Cucurbita maxima seeds methanolic extract (ME) against protoscolices of hydatid cyst in-vitro. Also, an in vivo assay was designed to prove the preventive effects of the extract. Materials and methods: For this work, Two different concentrations (25 and 50 mg/ml) of the C. maxima seeds ME were used in various exposure times (10, 20, 30, 40, 50, and 60 min). Additionally, thirty mice were infected intraperitoneally by injection of 1000 viable protoscolices and were divided into three groups with ten mice in each Group I (treated by Albendazole), group II (received 50 mg/ml of C. maxima seeds ME) and group III (untreated controls). Results: Overall, C. maxima seeds ME exhibited significant scolicidal effects in compared with control group (P<0.05). At a concentration of 50 mg/ml, the mortality percentage increased to 84.7%, 96.1% and 100% after 40, 50 and 60 minutes, respectively. Also, the obtain data in necropsy demonstrated that C. maxima seeds ME have an inhibitory effect on the hydatid cyst development. No hydatid cyst formation observed in mice treated with C. maxima seeds ME (50 mg/ml) versus control group which hydatid cyst occurred in 6 (from 10) mice. Conclusion: The current investigation indicated that applying C. maxima seeds ME could be considered as a potential scolicidal agent due to being economical, safer and non-toxic compared to the reference chemical drugs. However, further studies on probably active compounds and also to the determination of its mode of action on parasites are required