A design method based on the tree-model structure for topology update is presented. The routing tree of every node in network is built by defining the data structure and is used to save the topology information of nei...A design method based on the tree-model structure for topology update is presented. The routing tree of every node in network is built by defining the data structure and is used to save the topology information of neighbor nodes. The node topology update is accomplished by exchanging their routing trees. For saving the precious wireless bandwidth, the routing tree is sparsely shaped before sending by pruning the redundant routing information. Then, the node topology update is implemented by using algorithms of inserting and deleting routing sub-trees.展开更多
An improved heuristic algorithm is developed which can optimize the multicast routing under the condition that both delay and bandwidth are constrained. Performance analysis and computer simulation show that the routi...An improved heuristic algorithm is developed which can optimize the multicast routing under the condition that both delay and bandwidth are constrained. Performance analysis and computer simulation show that the routing mechanism can successfully solve the QoS problem in the case of many-to-many cast session. The scheme can make the cost of routing tree optimized and the bandwidth and end-to-end delay guaranteed. Because complexity of algorithm is limited, it is suitable to deal with networks of large size.展开更多
Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential time.Recently,there has been growing interest in end-t...Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential time.Recently,there has been growing interest in end-to-end deep neural networks for solving routing problems.However,such methods typically produce sequences of vertices,which make it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges,as in various spanning tree problems.In this paper,we propose NeuroPrim,a novel framework for solving various spanning tree problems by defining a Markov decision process for general combinatorial optimization problems on graphs.Our approach reduces the action and state space using Prim's algorithm and trains the resulting model using REINFORCE.We apply our framework to three difficult problems on the Euclidean space:the degree-constrained minimum spanning tree problem,the minimum routing cost spanning tree problem and the Steiner tree problem in graphs.Experimental results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 vertices.Additionally,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,000.Our results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.展开更多
A routing tree for a set of tasks is a decision tree which assigns the tasks to their destinationsaccording to the features of the tasks. A weighted routing tree is one with costs attached to each linkof the tree. Lin...A routing tree for a set of tasks is a decision tree which assigns the tasks to their destinationsaccording to the features of the tasks. A weighted routing tree is one with costs attached to each linkof the tree. Links of the same feature have the same cost. It is proved that the problem of finding ?routing tree of the minimum cost for a given set of tasks of two features is NP-complete.展开更多
文摘A design method based on the tree-model structure for topology update is presented. The routing tree of every node in network is built by defining the data structure and is used to save the topology information of neighbor nodes. The node topology update is accomplished by exchanging their routing trees. For saving the precious wireless bandwidth, the routing tree is sparsely shaped before sending by pruning the redundant routing information. Then, the node topology update is implemented by using algorithms of inserting and deleting routing sub-trees.
文摘An improved heuristic algorithm is developed which can optimize the multicast routing under the condition that both delay and bandwidth are constrained. Performance analysis and computer simulation show that the routing mechanism can successfully solve the QoS problem in the case of many-to-many cast session. The scheme can make the cost of routing tree optimized and the bandwidth and end-to-end delay guaranteed. Because complexity of algorithm is limited, it is suitable to deal with networks of large size.
基金supported by National Key R&D Program of China(Grant No.2021YFA1000403)National Natural Science Foundation of China(Grant No.11991022)+1 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA27000000)the Fundamental Research Funds for the Central Universities。
文摘Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential time.Recently,there has been growing interest in end-to-end deep neural networks for solving routing problems.However,such methods typically produce sequences of vertices,which make it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges,as in various spanning tree problems.In this paper,we propose NeuroPrim,a novel framework for solving various spanning tree problems by defining a Markov decision process for general combinatorial optimization problems on graphs.Our approach reduces the action and state space using Prim's algorithm and trains the resulting model using REINFORCE.We apply our framework to three difficult problems on the Euclidean space:the degree-constrained minimum spanning tree problem,the minimum routing cost spanning tree problem and the Steiner tree problem in graphs.Experimental results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 vertices.Additionally,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,000.Our results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.
基金This research was supported in part by the NSF grants DCB-8501226 and DCR-8696135. Part of this work was done while the first author was at the Mathematical Sciences Research Institute, Berkeley, California, and while the second author was at the Departm
文摘A routing tree for a set of tasks is a decision tree which assigns the tasks to their destinationsaccording to the features of the tasks. A weighted routing tree is one with costs attached to each linkof the tree. Links of the same feature have the same cost. It is proved that the problem of finding ?routing tree of the minimum cost for a given set of tasks of two features is NP-complete.
