We present a simple combinatorial 2-approximation algorithm for a minimum weight (simple) cycle in an undirected graph with nonnegative integer edge weights in the range { 1,2,...,M}. This algorithm runs in time O(n2logn logM).\\mathcal{O}(n^2\\log n \\log M)....
On the other hand, no algorithm working in Õ(Wn ω) time was previously known for undirected graphs with negative weights. Furthermore, our algorithm for a given directed or undirected graph detects whether it contains a negative weight cycle within the same running time. Computing ...
In order to store and handle the UCS, we propose a two-level data structure which is efficient for storage and easy to process. We also pointed several practical applications for our shortest cycle algorithms and the UCS data structure. This is a preview of subscription content, log in via...
We study the problem of determining a shortest cycle of even length (or of odd length, respectively). For cycles of odd length we get the same complexity as for determining a shortest cycle of a graph i. e. 0 (| V |·| E |) in the case of unweighted graphs and 0 (| V | 3 ...
Graph Theory—An Algorithmic Approach, Academic Press, New York (1975) Ch. 8 Google Scholar [3] S. Even Graph Algorithms, Computer Science Press, Rockville, MD (1979) Google Scholar [4] R.M. Karp A characterization of the minimum cycle mean in a digraph Discrete Math., 23 (1978), pp...
just move on.The Nya graph is an undirected graph with "layers". Each node in the graph belongs to a layer, there are N nodes in total.You can move from any node in layer x to any node in layer x + 1, with cost C, since the roads are bi-directional, moving from layer x + ...
Theshortestpath,shortestpathtree, anddistancesfunctions do not support undirected graphs with negative edge weights, or more generally any graph containing a negative cycle, for these reasons: Anegative cycleis a path that leads from a node back to itself, with the sum of the edge weights on ...
If a negative cycle is on a path between two nodes, then no shortest path exists between the nodes, since a shorter path can always be found by traversing the negative cycle. A single negative edge weight in an undirected graph creates a negative cycle....
u G.origin(e) Can be extended to detect z G.opposite(u,e) a negative-weight cycle if it r getDistance (u) + weight(e) exists if r getDistance (z) How? setDistance(z,r) 29 Bellman-Ford Example Nodes are labeled with their d(v) values 8 0 4 8 0 4 -2...
The rest of the sections are as described above; we conclude in Section 8. 1.2. Related Previous Work Thomassen [23] was the first to give a polynomial-time algorithm for finding a shortest non-separating and a shortest non-contractible cycle in a graph on a surface; see also Chapter 4 ...