Classification and Traversal Algorithmic Techniques for Optimization Proble...

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

英文文献：Classification and Traversal Algorithmic Techniques for Optimization Problems on Directed Hyperpaths
英文文献作者：Giorgio Ausiello,Giuseppe F. Italiano,Luigi Laura,Umberto Nanni,Fabiano Sarracco
英文文献摘要：
Directed hypergraphs are used in several applications to model different combinatorial struc- tures. A directed hypergraph is defined by a set of nodes and a set of hyperarcs, each connecting a set of source nodes to a single target node. A hyperpath, similarly to the notion of path in directed graphs, consists of a connection among nodes using hyperarcs. Unlike paths in graphs, however, hyperpaths are suitable of many different definitions of measure, which have been used in a wide set of applications. Not surprisingly, depending on the considered measure function the cost of finding optimal hyperpaths may range from NP-hard to linear time. A first solution for finding optimal hyperpaths in case of a superior functions (SUP) can be found in a seminal work by Knuth [Knu77], which generalizes Dijkstra's Algorithm [Dij59] to deal with a grammar problem. This solution is further extended by Ramalingam and Reps [RR96] to deal with weakly superior functions (WSUP). Dijkstra's priority queue can find optimal paths or hyperpaths if the measure function complies two hypotheses: it is monotone with respect to all its arguments and (multidimensional) triangle inequality holds. We show that monotonicity - alone - is sufficient to guarantee interesting properties, and to make some optimization algorithms effective. Hence we introduce the generalized superior function (GSUP), and consider the symmetrical classes of inferior functions, giving rise to a hierarchy of classes of optimization problems on directed hypergraphs. After showing that some measure functions might induce cycles in optimal hyperpaths, we come up to another taxonomy of measure functions, based on the structure of the optimal hyperpaths they determine, and relate the two hierarchies. Finally we introduce a general algorithmic pattern for the single-source optimal hyperpath problem encompassing existing and new algorithms, and compare their effectiveness in various cases, including the case of optimal cyclic hyperpaths.

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖