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Conventional cancer treatment is mainly based on the surgical removal of the tumor followed by radiotherapy and/or chemotherapy. When surgical removal is not possible, radiotherapy and, less often, chemotherapy is the only way to treat patients. However, despite significant progress in understanding the molecular mechanisms of carcinogenesis and developments in modern radiotherapy techniques, radiotherapy (alone or in combination) does not always guarantee treatment success. One of the main causes is the radioresistance of cancer cells. Increasing the radiosensitivity of cancer cells improves the processes leading to their elimination during radiotherapy and prolonging the survival of cancer patients. In order to enhance the effect of radiotherapy in the treatment of radioresistant neoplasms, radiosensitizers are used. In clinical practice, synthetic radiosensitizers are commonly applied, but scientists have recently focused on using natural products (phytocompounds) as adjuvants in radiotherapy. In this review article, we only discuss naturally occurring radiosensitizers currently in clinical trials (paclitaxel, curcumin, genistein, and papaverine) and those whose radiation sensitizing effects, such as resveratrol, have been repeatedly confirmed by many independent studies. [ABSTRACT FROM AUTHOR]

We consider the single-machine time-dependent scheduling problem with linearly deteriorating jobs arriving over time. Each job i is associated with a release time r i and a processing time p i (s i) = α i + β i s i , where α i , β i > 0 are parameters and s i is the job's start time. In this setting, the approximability of both single-machine minimum makespan and total completion time problems remains open. We develop new bounds and approximation results for the special case of the problems with uniform deterioration, i.e. β i = β , for each i. The main contribution is a O (1 + 1 / β) -approximation algorithm for the makespan problem and a O (1 + 1 / β 2) approximation algorithm for the total completion time problem. Further, we propose greedy constant-factor approximation algorithms for instances with β = O (1 / n) and β = Ω (n) , where n is the number of jobs. Our analysis is based on an approach for comparing computed and optimal schedules via bounding pseudomatchings. [ABSTRACT FROM AUTHOR]

A garden is populated by n bamboos, each with its own daily growth rate. The Bamboo Garden Trimming Problem (BGT) is to design for a robotic gardener a perpetual schedule of cutting bamboos to keep the elevation of the garden as low as possible. The frequency of cutting is constrained by the time needed to move from one bamboo to the next, which is one day in Discrete BGT and is defined by the distance between the two bamboos in Continuous BGT. The bamboo garden is a metaphor for a collection of machines which have to be serviced, with different frequencies, by a robot which can service only one machine at a time. For Discrete BGT, we show tighter approximation algorithms, with one of them settling a long-standing conjecture about the related Pinwheel problem. For Continuous BGT, we propose approximation algorithms which achieve logarithmic approximation ratios. [ABSTRACT FROM AUTHOR]