Stochastic k-Server: How Should Uber Work?

In this paper we study a stochastic variant of the celebrated $k$-server problem. In the k-server problem, we are required to minimize the total movement of k servers that are serving an online sequence of $t$ requests in a metric. In the stochastic setting we are given t independent distributions in advance, and at every time step i a request is drawn from P_i. Designing the optimal online algorithm in such setting is NP-hard, therefore the emphasis of our work is on designing an approximately optimal online algorithm. We first show a structural characterization for a certain class of non-adaptive online algorithms. We prove that in general metrics, the best of such algorithms has a cost of no worse than three times that of the optimal online algorithm. Next, we present an integer program that finds the optimal algorithm of this class for any arbitrary metric. Finally by rounding the solution of the linear relaxation of this program, we present an online algorithm for the stochastic k-server problem with an approximation factor of $3$ in the line and circle metrics and factor of O(log n) in general metrics. In this way, we achieve an approximation factor that is independent of k, the number of servers. Moreover, we define the Uber problem, motivated by extraordinary growth of online network transportation services. In the Uber problem, each demand consists of two points -a source and a destination- in the metric. Serving a demand is to move a server to its source and then to its destination. The objective is again minimizing the total movement of the k given servers. It is not hard to show that given an alpha-approximation algorithm for the k-server problem, we can obtain a max{3,alpha}-approximation algorithm for the Uber problem. Motivated by the fact that demands are usually highly correlated with the time (e.g. what day of the week or what time of the day the demand is arrived), we study the stochastic Uber problem. Using our results for stochastic k-server we can obtain a 3-approximation algorithm for the stochastic Uber problem in line and circle metrics, and a O(log n)-approximation algorithm for a general metric of size n. Furthermore, we extend our results to the correlated setting where the probability of a request arriving at a certain point depends not only on the time step but also on the previously arrived requests

Greedy Algorithms for Online Survivable Network Design

In an instance of the network design problem, we are given a graph G=(V,E), an edge-cost function c:E -> R^{>= 0}, and a connectivity criterion. The goal is to find a minimum-cost subgraph H of G that meets the connectivity requirements. An important family of this class is the survivable network design problem (SNDP): given non-negative integers r_{u v} for each pair u,v in V, the solution subgraph H should contain r_{u v} edge-disjoint paths for each pair u and v. While this problem is known to admit good approximation algorithms in the offline case, the problem is much harder in the online setting. Gupta, Krishnaswamy, and Ravi [Gupta et al., 2012] (STOC\u2709) are the first to consider the online survivable network design problem. They demonstrate an algorithm with competitive ratio of O(k log^3 n), where k=max_{u,v} r_{u v}. Note that the competitive ratio of the algorithm by Gupta et al. grows linearly in k. Since then, an important open problem in the online community [Naor et al., 2011; Gupta et al., 2012] is whether the linear dependence on k can be reduced to a logarithmic dependency. Consider an online greedy algorithm that connects every demand by adding a minimum cost set of edges to H. Surprisingly, we show that this greedy algorithm significantly improves the competitive ratio when a congestion of 2 is allowed on the edges or when the model is stochastic. While our algorithm is fairly simple, our analysis requires a deep understanding of k-connected graphs. In particular, we prove that the greedy algorithm is O(log^2 n log k)-competitive if one satisfies every demand between u and v by r_{uv}/2 edge-disjoint paths. The spirit of our result is similar to the work of Chuzhoy and Li [Chuzhoy and Li, 2012] (FOCS\u2712), in which the authors give a polylogarithmic approximation algorithm for edge-disjoint paths with congestion 2. Moreover, we study the greedy algorithm in the online stochastic setting. We consider the i.i.d. model, where each online demand is drawn from a single probability distribution, the unknown i.i.d. model, where every demand is drawn from a single but unknown probability distribution, and the prophet model in which online demands are drawn from (possibly) different probability distributions. Through a different analysis, we prove that a similar greedy algorithm is constant competitive for the i.i.d. and the prophet models. Also, the greedy algorithm is O(log n)-competitive for the unknown i.i.d. model, which is almost tight due to the lower bound of [Garg et al., 2008] for single connectivity

Online Weighted Degree-Bounded Steiner Networks via Novel Online Mixed Packing/Covering

We design the first online algorithm with poly-logarithmic competitive ratio for the edge-weighted degree-bounded Steiner forest (EW-DB-SF) problem and its generalized variant. We obtain our result by demonstrating a new generic approach for solving mixed packing/covering integer programs in the online paradigm. In EW-DB-SF, we are given an edge-weighted graph with a degree bound for every vertex. Given a root vertex in advance, we receive a sequence of terminal vertices in an online manner. Upon the arrival of a terminal, we need to augment our solution subgraph to connect the new terminal to the root. The goal is to minimize the total weight of the solution while respecting the degree bounds on the vertices. In the offline setting, edge-weighted degree-bounded Steiner tree (EW-DB-ST) and its many variations have been extensively studied since early eighties. Unfortunately, the recent advancements in the online network design problems are inherently difficult to adapt for degree-bounded problems. In particular, it is not known whether the fractional solution obtained by standard primal-dual techniques for mixed packing/covering LPs can be rounded online. In contrast, in this paper we obtain our result by using structural properties of the optimal solution, and reducing the EW-DB-SF problem to an exponential-size mixed packing/covering integer program in which every variable appears only once in covering constraints. We then design a generic integral algorithm for solving this restricted family of IPs. As mentioned above, we demonstrate a new technique for solving mixed packing/covering integer programs. Define the covering frequency k of a program as the maximum number of covering constraints in which a variable can participate. Let m denote the number of packing constraints. We design an online deterministic integral algorithm with competitive ratio of O(k*log(m)) for the mixed packing/covering integer programs. We prove the tightness of our result by providing a matching lower bound for any randomized algorithm. We note that our solution solely depends on m and k. Indeed, there can be exponentially many variables. Furthermore, our algorithm directly provides an integral solution, even if the integrality gap of the program is unbounded. We believe this technique can be used as an interesting alternative for the standard primal-dual techniques in solving online problems

A green and efficient method for the preparation of 3, 4- dihydropyrimidin-2(1H)-ones using quaternary ammonium- treated clay in water

Abstract: In this study, a variety of 3, 4-dihydropyrimidin-2(1H)-ones derivatives were synthesized via three-component Biginelli reaction. The quaternary ammonium-treated clay -catalyzed process proved to be simple, efficient, and environmentally friendly

Correlation of Midkine Serum Level with Pro- and Anti-Inflamatory Cytokines in Multiple Sclerosis

Background: Midkine (MK) is a heparin-binding growth factor with promoting effects in inflammatory responses through enhancing leukocytes migration. Objective: To study the correlation between MK serum levels and concentration of inflammatory cytokines in Multiple Sclerosis (MS) patients. Methods: We evaluated the MK level and its relationship with inflammatory cytokines (IL-17 and IL-23) and anti-inflammatory ones (IL-10 and TGF-beta) in multiple sclerosis (MS) patients. The serum concentrations of MK and cytokines were assessed by ELISA in 32 MS patients in comparison with 32 healthy subjects. Results: Our data showed that the MK concentration in MS patients is lower than healthy controls (341.15 +/- 40.71 Pg/ml vs. 620.15 +/- 98.61 Pg/ml, respectively, p= 0.015). We also observed a significant decrease in IL-10, IL-23, and TGF-beta cytokine levels in MS patients. There was a significant correlation between MK and IL-23 concentrations in our study (r = + 0.829, p <= 0.001). Conclusion: These results confirm a role for MK in inflammatory reactions in MS

Faster and Simpler Algorithm for Optimal Strategies of Blotto Game

In the Colonel Blotto game, which was initially introduced by Borel in 1921, two colonels simultaneously distribute their troops across different battlefields.The winner of each battlefield is determined independently by a winner-take-all rule. The ultimate payoff of each colonel is the number of battlefields he wins. This game is commonly used for analyzing a wide range of applications such as the U.S presidential election, innovative technology competitions, advertisements, etc. There have been persistent efforts for finding the optimal strategies for the Colonel Blotto game. After almost a century Ahmadinejad, Dehghani, Hajiaghayi, Lucier, Mahini, and Seddighin provided a poly-time algorithm for finding the optimal strategies. They first model the problem by a Linear Program (LP) with exponential number of constraints and use Ellipsoid method to solve it. However, despite the theoretical importance of their algorithm, it ishighly impractical. In general, even Simplex method (despite its exponential running-time) performs better than Ellipsoid method in practice. In this paper, we provide the first polynomial-size LP formulation of the optimal strategies for the Colonel Blotto game. We use linear extension techniques. Roughly speaking, we project the strategy space polytope to a higher dimensional space, which results in a lower number of facets for the polytope.We use this polynomial-size LP to provide a novel, simpler and significantly faster algorithm for finding the optimal strategies for the Colonel Blotto game. We further show this representation is asymptotically tight in terms of the number of constraints. We also extend our approach to multi-dimensional Colonel Blotto games, and implement our algorithm to observe interesting properties of Colonel Blotto; for example, we observe the behavior of players in the discrete model is very similar to the previously studied continuous model

Comparison of cartilage specific markers in articular and differentiated chondrocytes in pellet system.

Abstract Autologous cartilage replacement has the inherent advantage that the transplanted tissue is immunogenically neutral. However, chondrocyte isolation, proliferation, and dedifferentiation limitations resulted in the search for a cell type that would overcome the aforementioned limitations. Here we investigated if adipose-derived stem cells (ADSCs), which are easy to isolate in large quantities, in combination with a three dimensional culture system and growth factor would be a suitable alternative for autologous cartilage ..

Nonlinear optical properties of 3,3′-biindole 2,2′(1H,1′H)-dione derivatives

The Z-scan instrument was used to study the nonlinear optical (NLO) properties of the derivatives of 3,3′-biindole 2,2′(1H,1′H)-dione, with different substitutions such as bromine, methyl, and phenyl groups. Specifically, the nonlinear absorption coefficient, β, nonlinear refraction index, n2, have been extracted and reverse saturation absorption and self-defocusing phenomena were investigated. It is observed that the presence of bromine in the compound structure can reduce the NLO properties. The reduction of dipole moment with bromine substitutions in the compound structure was confirmed with the quantum calculation. The NLO properties of the biindole derivatives related to the thermo-optic coefficient and dipole moment of the compound. Overall, our findings indicate that the biindole derivatives are promising candidates for NLO absorption materials.Peer reviewe