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The multi objective shortest path (MOSP) problem, crucial in various practical domains, seeks paths that optimize multiple objectives. Due to its high computational complexity, numerous parallel heuristics have been developed for static networks. However, real-world networks are often dynamic where the network topology changes with time. Efficiently updating the shortest path in such networks is challenging, and existing algorithms for static graphs are inadequate for these dynamic conditions, necessitating novel approaches. Here, we first develop a parallel algorithm to efficiently update a single objective shortest path (SOSP) in fully dynamic networks, capable of accommodating both edge insertions and deletions. Building on this, we propose DynaMOSP, a parallel heuristic for Dynamic Multi Objective Shortest Path searches in large, fully dynamic networks. We provide a theoretical analysis of the conditions to achieve Pareto optimality. Furthermore, we devise a dedicated shared memory CPU implementation along with a version for heterogeneous computing environments. Empirical analysis on eight real-world graphs demonstrates that our method scales effectively. The shared memory CPU implementation achieves an average speedup of 12.74× and a maximum of 57.22×, while on an Nvidia GPU, it attains an average speedup of 69.19×, reaching up to 105.39× when compared to state-of-the-art techniques.
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Finding shortest and nearly shortest path nodes in large substantially incomplete networks by hyperbolic mapping
Abstract Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Computing shortest paths is a straightforward task when the network of interest is fully known, and there are a plethora of computational algorithms for this purpose. Unfortunately, our maps of most large networks are substantially incomplete due to either the highly dynamic nature of networks, or high cost of network measurements, or both, rendering traditional path finding methods inefficient. We find that shortest paths in large real networks, such as the network of protein-protein interactions and the Internet at the autonomous system level, are not random but are organized according to latent-geometric rules. If nodes of these networks are mapped to points in latent hyperbolic spaces, shortest paths in them align along geodesic curves connecting endpoint nodes. We find that this alignment is sufficiently strong to allow for the identification of shortest path nodes even in the case of substantially incomplete networks, where numbers of missing links exceed those of observable links. We demonstrate the utility of latent-geometric path finding in problems of cellular pathway reconstruction and communication security.
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- Award ID(s):
- 1741355
- PAR ID:
- 10391735
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 14
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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