关于Fagelian Hamilton图的探讨
Exploration of Faulty Hamiltonian Graphs
摘要：
我们考虑网络的探索问题，其中一些边缘是错误的。一个移动代理，位于一个起始节点，不知道哪些边缘是错误的，探索连接的无故障组件的这个节点，通过访问它的所有节点。探索的代价是边遍历的次数。对于给定的网络和给定的起始节点，探索算法的开销是其成本与知道故障位于何处的最优算法的成本的最坏情况比率（在所有故障配置上进行）。对于给定的网络和给定的起始节点，如果在不知道故障位置的情况下，一个搜索算法的开销是所有搜索算法中最小的，则称该搜索算法是完全竞争的。我们设计了一个完全竞争的探索算法的任何环，并表明，网络模型的哈密顿图，任何DFS探索的开销是最多10/9倍以上的一个完全竞争的算法。此外，对于大小至少为24的哈密尔顿图，此开销比完全竞争算法的开销大不到6%。
英文摘要：
We consider the problem of exploration of networks, some of whose edges are faulty. A mobile agent, situated at a starting node and unaware of which edges are faulty, has to explore the connected fault-free component of this node by visiting all of its nodes. The cost of the exploration is the number of edge traversals. For a given network and given starting node, the overhead of an exploration algorithm is the worst-case ratio (taken over all fault configurations) of its cost to the cost of an optimal algorithm which knows where faults are situated. An exploration algorithm, for a given network and given starting node, is called perfectly competitive if its overhead is the smallest among all exploration algorithms not knowing the location of faults. We design a perfectly competitive exploration algorithm for any ring, and show that, for networks modeled by hamiltonian graphs, the overhead of any DFS exploration is at most 10/9 times larger than that of a perfectly competitive algorithm. Moreover, for hamiltonian graphs of size at least 24, this overhead is less than 6% larger than that of a perfectly competitive algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
