The cake-cutting problem provides a model for addressing fair allocation of a divisible resource (metaphorically, the cake) among agents with distinct preferences.
As scientists and engineers, we have long aimed at solving real-time problems such as detecting and localizing objects seen by our video recorder or at least something like Pokemon's Animedex.
The relation between math and algorithmics is very old. In a sense, one can even argue that mathematics was created to show that some already known algorithms worked in all cases and not only on some examples.
Randomness is a remarkably powerful tool in the design of algorithms. By giving algorithms the ability to use random bits and letting them err with some small probability, we can solve many computational problems with remarkable efficiency.
The problem of learning arithmetic circuits is the following: given a polynomial as a black box that is promised to have a small arithmetic circuit computing it, can we find this arithmetic circuit?
Partial function extension is a basic problem that underpins multiple research topics in optimization, including learning, property testing, and game theory.
Randomness is a vital tool and resource in both classical and quantum information processing. However, constructing random bits is expensive, and hence minimising their use is desirable.
Secure message transmission and Byzantine agreement have been studied extensively in incomplete networks. However, information theoretically secure multiparty computation (MPC) in incomplete networks is less well understood.
