for Sublinear Time Maximum Inner Product Search (MIPS)

... which is an instance of the standard MIPS problem. It should be noted that we do not have control over the norm of the learned vector, i.e., ∥vj ∥2 , which often has a wide range in practice [13]. If there are N items to recommend, solving (3) requires computing N inner products. Recommendation syst ...

... which is an instance of the standard MIPS problem. It should be noted that we do not have control over the norm of the learned vector, i.e., ∥vj ∥2 , which often has a wide range in practice [13]. If there are N items to recommend, solving (3) requires computing N inner products. Recommendation syst ...

Core Node Location Problem - Robert B. Willumstad School of

... regenerator location problem. They prove that the problem is NP-Complete and propose three heuristics for solving it suboptimally. They also show how to model it as a Steiner arborescence problem with a unit degree constraint on the root node. In this paper we propose two related mixed integer formu ...

... regenerator location problem. They prove that the problem is NP-Complete and propose three heuristics for solving it suboptimally. They also show how to model it as a Steiner arborescence problem with a unit degree constraint on the root node. In this paper we propose two related mixed integer formu ...

# Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science and mathematics that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other. A computational problem is understood to be a task that is in principle amenable to being solved by a computer, which is equivalent to stating that the problem may be solved by mechanical application of mathematical steps, such as an algorithm.A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Other complexity measures are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.Closely related fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem. More precisely, it tries to classify problems that can or cannot be solved with appropriately restricted resources. In turn, imposing restrictions on the available resources is what distinguishes computational complexity from computability theory: the latter theory asks what kind of problems can, in principle, be solved algorithmically.