71 lines
3.1 KiB
Rust
71 lines
3.1 KiB
Rust
//! Mesh connectivity abstractions.
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//!
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//! A satellite mesh is a set of terminals that reach each other through
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//! links, some of which are satellite links and some of which are ground
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//! links. This crate provides the abstractions that a mesh application needs
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//! on top of a topology: which terminals can reach which others, how many
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//! independent ways there are to do so, and which links are critical.
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//!
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//! The three questions this crate answers:
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//!
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//! - **Reachability**: the set of terminals reachable from a given one.
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//! - **Redundancy**: how many independent paths join two terminals, which is
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//! the number of links that can fail independently. This is the
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//! edge-connectivity of the graph, by Menger's theorem.
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//! - **Criticality**: the links whose removal would separate the mesh, which
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//! are the ones a network operator must protect.
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//!
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//! The redundancy computation is exact for the small graphs a satellite mesh
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//! presents. It uses the edge version of Menger's theorem, computing the
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//! connectivity from a sequence of maximum flow problems, each of unit
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//! capacity.
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//!
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//! Source: Menger's theorem, and the reduction of edge connectivity to
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//! maximum flow, as given in Cormen et al., *Introduction to Algorithms*,
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//! 3rd edition, MIT Press, 2009, chapter 26.
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//!
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//! ```
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//! use apsis_mesh::Mesh;
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//! use apsis_topology::Topology;
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//!
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//! // Three terminals in a ring, so each pair has two independent paths.
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//! let mut topology = Topology::new(3);
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//! topology.add_bidirectional_edge(0, 1, 1.0).expect("the nodes exist");
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//! topology.add_bidirectional_edge(1, 2, 1.0).expect("the nodes exist");
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//! topology.add_bidirectional_edge(2, 0, 1.0).expect("the nodes exist");
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//!
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//! let mesh = Mesh::new(topology);
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//! assert!(mesh.is_connected());
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//! assert_eq!(mesh.edge_connectivity(0, 1), Some(2));
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//! ```
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//!
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//! 网格连通性抽象。
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//!
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//! 卫星网格是一组经链路互相到达的终端，其中一些是卫星链路、一些是地面链路。本
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//! crate 提供网格应用在拓扑之上所需的抽象：哪些终端能到达哪些其他终端、有多少条
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//! 独立路径可以做到，以及哪些链路是关键。
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//!
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//! 本 crate 回答的三个问题：
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//!
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//! - **可达性**：自某给定终端可达的终端集合。
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//! - **冗余度**：连接两个终端的独立路径条数，即可独立失效的链路数。依 Menger 定理，
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//! 它是该图的边连通度。
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//! - **关键性**：移除后会切开网格的那些链路，即网络运营者必须保护的链路。
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//!
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//! 冗余度计算对卫星网格所呈现的小图是精确的。它使用 Menger 定理的边版本，从一
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//! 系列单位容量的最大流问题计算连通度。
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//!
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//! 出处：Menger 定理，以及把边连通度归约为最大流，见 Cormen 等，
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//! *Introduction to Algorithms*，第 3 版，MIT Press，2009，第 26 章。
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#![forbid(unsafe_code)]
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#![deny(missing_docs)]
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mod connectivity;
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mod mesh;
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pub use connectivity::{edge_connectivity, reachable_from, strongly_connected_components};
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pub use mesh::{CriticalLink, Mesh, MeshSummary};
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pub use apsis_topology::{Topology, TopologySeries};
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