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In a partially connected mesh topology, there are at least two nodes with two or more paths between them to provide redundant paths in case the link providing one of the paths fails. Decentralization is often used to compensate for the single-point-failure disadvantage that is present when using a single device as a central node (e.g., in star ...
The network is typically quite reliable, as there is often more than one path between a source and a destination in the network. Although mostly used in wireless situations, this concept can also apply to wired networks and to software interaction. A mesh network whose nodes are all connected to each other is a fully connected network. Fully ...
The K (>2) versions are similarly obtained, e.g., the vertices of the shortest edge disjoint pair of paths (except for the source and destination vertices) are split, with the vertices in each split pair connected to each other with arcs of zero weight as well as the external edges in a similar manner [8][9]. The algorithms presented for ...
The rest of the graph is connected. In an undirected graph G, two vertices u and v are called connected if G contains a path from u to v. Otherwise, they are called disconnected. If the two vertices are additionally connected by a path of length 1 (that is, they are the endpoints of a single edge), the vertices are called adjacent.
A central problem in algorithmic graph theory is the shortest path problem. Hereby, the problem of finding the shortest path between every pair of nodes is known as all-pair-shortest-paths (APSP) problem. As sequential algorithms for this problem often yield long runtimes, parallelization has shown to be beneficial in this field. In this ...
In computer networking, hypercube networks are a type of network topology used to connect and route data between multiple processing units or computers. Hypercube networks consist of 2 m nodes, which form the vertices of squares to create an internetwork connection. A hypercube is basically a multidimensional mesh network with two nodes in each ...
– let p u be the shortest cost path in B with cost C – B = B − {p u}, count u = count u + 1 – if u = t then P = P U {p u} – if count u ≤ K then for each vertex v adjacent to u: – let p v be a new path with cost C + w(u, v) formed by concatenating edge (u, v) to path p u – insert p v into B return P
A number of other protection schemes such as the use of pre-emptible paths, or only partially diverse backup paths, can be implemented. Finally, multiple diverse routes can be designed so that a connection has multiple recovery routes and can recover even after multiple failures (examples of mesh networks across the Atlantic and Pacific oceans ...