Buyback Problem - Approximate matroid intersection with cancellation costs

In the buyback problem, an algorithm observes a sequence of bids and must decide whether to accept each bid at the moment it arrives, subject to some constraints on the set of accepted bids. Decisions to reject bids are irrevocable, whereas decisions to accept bids may be canceled at a cost that is a fixed fraction of the bid value. Previous to our work, deterministic and randomized algorithms were known when the constraint is a matroid constraint. We extend this and give a deterministic algorithm for the case when the constraint is an intersection of $k$ matroid constraints. We further prove a matching lower bound on the competitive ratio for this problem and extend our results to arbitrary downward closed set systems. This problem has applications to banner advertisement, semi-streaming, routing, load balancing and other problems where preemption or cancellation of previous allocations is allowed

Perfectly Secure Message Transmission Tolerating Mixed Adversary

In this paper, we study the issues related to the possibility, feasibility and optimality for perfectly secure message transmission (PSMT) in an undirected synchronous network, under the influence of a mixed adversary having unbounded computing power, who can corrupt some of the nodes in the network in Byzantine, fail-stop and passive fashion respectively. Specifically, we answer the following questions: (a) Possibility: Given a network and a mixed adversary, what are the necessary and sufficient conditions for the existence of any PSMT protocol over the network tolerating the adversary? (b) Feasibility: Once the existence of a protocol is ensured, then does there exist a polynomial time and efficient protocol on the given network? (c) Optimality: Given a message of specific length, what is the minimum communication complexity (lower bound) needed by any PSMT protocol to transmit the message and how to design a polynomial time protocol whose total communication complexity matches the lower bound on the communication complexity? We answer the above questions by considering two different types of mixed adversary, namely static mixed adversary and mobile mixed adversary. Intuitively, it is more difficult to tolerate a mobile mixed adversary (who can corrupt different set of nodes during different stages of the protocol) in comparison to its static counter part (who corrupts the same set of nodes throughout the protocol). However, surprisingly, we show that the connectivity requirement in the network and lower bound on communication complexity of PSMT protocols is same against both static and mobile mixed adversary. To design our protocols against static and mobile mixed adversary, we use several new techniques, which are of independent interest

Promotive and Preventive Eye Care in Ayurveda and Morden view

Your eyes are an important part of your head . Most people rely on their eyes to see and make sense of the world around them , but some eye disesse can lead to vision loss , so it’s important to identify and treat eye disease as early as possible. There are five sense organs i.e. eye, ear, nose, tongue and skin. Among these sense organs, Ayurveda gives prime importance to the eye. It says “SarvendriyaanamNayanamPradhanamâ€. Eyes allow to understand and navigate the world around you. Suffering from eye disorders with uncorrected refractive error in children result into adverse effect on quality of life & signiï¬cantly affect their vision, education and psychosocial development. Most of people pay attention to their eyes only if they have eye problems. However, the hours spent in reading, writing, watching TV, using multimedia mobile and working on computers take their toll on eye health. Working in artificial light (either dim light or bright light) is another  culprit for deterioration of eye health. If 100 students of Indian school aged more than seven years are screened, 14 of them are likely to need spectacles. In Ayurveda, selected classical daily regimens like Netraprakshalna(eye wash), Anjana(Collyrium), Snana(Bath), Padabhyanga(Foot massage with oil), Nasya(nasal application of drugs), wholesome and unholsome dietetic are promoted as high-end measures for the maintenance of eye health. Various NetraVyayamas(eye exercises), Yogasanas, Pranayamas, Netiand Tratakaare also said to be beneficial for the same cause. Major Ayurvedicpromotive measures and perceptions regarding maintenance of eye health and prevention of eye disorders are explored in this article. The aim of this review is to spreads the awareness of simple visual health promotive procedures in Ayurveda