A NOTE ON HARDNESS OF MULTIPROCESSOR SCHEDULING WITH SCHEDULING SOLUTION SPACE TREE

We study the computational complexity of the non-preemptive scheduling problem of a listof independent jobs on a set of identical parallel processors with a makespan minimizationobjective. We make a maiden attempt to explore the combinatorial structure showing theexhaustive solution space of the problem by defining the Scheduling Solution Space Tree(SSST) data structure. The properties of the SSST are formally defined and characterizedthrough our analytical results. We develop a unique technique to show the problemNP using the SSST and the Weighted Scheduling Solution Space Tree (WSSST) datastructures. We design the first non-deterministic polynomial-time algorithm named MagicScheduling (MS) for the problem based on the reduction framework. We also define anew variant of multiprocessor scheduling by including the user as an additional inputparameter. We formally establish the complexity class of the variant by the reductionprinciple. Finally, we conclude the article by exploring several interesting open problemsfor future research investigation

Semi-online Scheduling with Lookahead

The knowledge of future partial information in the form of a lookahead to design efficient online algorithms is a theoretically-efficient and realistic approach to solving computational problems. Design and analysis of semi-online algorithms with extra-piece-of-information (EPI) as a new input parameter has gained the attention of the theoretical computer science community in the last couple of decades. Though competitive analysis is a pessimistic worst-case performance measure to analyze online algorithms, it has immense theoretical value in developing the foundation and advancing the state-of-the-art contributions in online and semi-online scheduling. In this paper, we study and explore the impact of lookahead as an EPI in the context of online scheduling in identical machine frameworks. We introduce a $k$-lookahead model and design improved competitive semi-online algorithms. For a $2$-identical machine setting, we prove a lower bound of $\frac{4}{3}$ and design an optimal algorithm with a matching upper bound of $\frac{4}{3}$ on the competitive ratio. For a $3$-identical machine setting, we show a lower bound of $\frac{15}{11}$ and design a $\frac{16}{11}$-competitive improved semi-online algorithm.Comment: 14 pages, 1 figur

Multiorgan dysfunction (MOD) in falciparum malaria in children: a study from high endemic area of Southern Odisha

Background: To find out the prevalence of multiorgan dysfunction in cases of severe falciparum malaria in children, correlating the organ dysfunction in different age group and relationship with case fatality rate (CFR).Methods: This prospective cross-sectional study was conducted from Jan 2014 to June 2016 in the Department of Pediatrics, Maharaja Krushna Chandra Gajapati medical college and hospital (MKCG MCH), Berhampur, Odisha, India. Total 340 cases belonging to 5yr age group. Hyperparasitemia (>10%) was detected in 12.35% cases. Cerebral malaria was most common organ dysfunction found in 1-5 years, followed by anaemia in 5-10 years, acute renal failure (ARF) in 10-14 years age group. Multiorgan dysfunction (MOD) was detected in 32.94% cases of severe malaria. Overall CFR was 8.82%, being directly proportional to no. of organ involvement, 31.81% with 4 organs and 100 % with five organs involvement respectively which was statistically significant.Conclusions: MOD is of grave outcome in severe Pf malaria increasing the case fatality rate proportionate to number of organs involved