multi-criteria shortest path problems (mspp) are called as np-hard. for mspps, a unique solution for optimizing all the criteria simultaneously will rarely exist in reality. algorithmic and approximation schemes are available to solve these problems; however, the complexity of these approaches often prohibits their implementation on real-world applications. this paper describes the development ...

We consider a variant of two-point Euclidean shortest path query problem: given a polygonal domain, build a data structure for two-point shortest path query, provided that query points always lie on the boundary of the domain. As a main result, we show that a logarithmic-time query for shortest paths between boundary points can be performed using Õ(n) preprocessing time and Õ(n) space where n i...

We study two speedup techniques for route planning in road networks: highway hierarchies (HH) and goal directed search using landmarks (ALT). It turns out that there are several interesting synergies. Highway hierarchies yield a way to implement landmark selection more efficiently and to store landmark information more space efficiently than before. ALT gives queries in highway hierarchies an e...

We introduce a framework for a class of algorithms solving shortest path related problems, such as the one-to-one shortest path problem, the one-to-many shortest paths pmblem and the minimum spanning tree problem, in the presence of obstacles. For these algorithms, the search space is restricted to a sparse strong connection graph which is implicitly represented and its searched portion is cons...

Null space Newton algorithms are efficient in solving the nonlinear equations arising in hydraulic analysis of water distribution networks. In this article, we propose and evaluate an inexact Newton method that relies on partial updates of the network pipes’ frictional headloss computations to solve the linear systems more efficiently and with numerical reliability. The update set parameters ar...

The null space property (NSP) and the restricted isometry property (RIP) are two properties which have received considerable attention in the compressed sensing literature. As the name suggests, NSP is a property that depends solely on the null space of the measurement procedure and as such, any two matrices which have the same null space will have NSP if either one of them does. On the other h...