Memoryless search algorithms in a network with faulty advice

Quantum Search with Advice

We consider the problem of search of an unstructured list for a marked element x, when one is given advice as to where x might be located, in the form of a probability distribution. The goal is to minimise the expected number of queries to the list made to find x, with respect to this distribution. We present a quantum algorithm which solves this problem using an optimal number of queries, up t...

Online Algorithms with Advice⋆

In online problems, the input forms a finite sequence of requests. Each request must be processed, i. e., a partial output has to be computed only depending on the requests having arrived so far, and it is not allowed to change this partial output subsequently. The aim of an online algorithm is to produce a sequence of partial outputs that optimizes some global measure. The most frequently used...

Communication algorithms with advice

We study the amount of knowledge about a communication network that must be given to its nodes in order to efficiently disseminate information. Our approach is quantitative: we investigate the minimum total number of bits of information (minimum size of advice) that has to be available to nodes, regardless of the type of information provided. We compare the size of advice needed to perform broa...

Online Algorithms with Advice

On Search for all d-MCs in a Network Flow

A number of problems in several areas such as power transmission and distribution, communication and transportation can be formulated as a stochastic-flow network (SFN). The system reliability of an SFN can be computed in terms of all the upper boundary points, called d-MinCuts (d-MCs). Several algorithms have been proposed to find all the d-MCs in an SFN. Here, some recent studies in the liter...