In this paper we consider a fundamental problem in the area of viral marketing, called Target Set Selection problem. We study the problem when the underlying graph is a block-cactus graph, a chordal graph or a Hamming graph. We show that if G is a block-cactus graph, then the Target Set Selection problem can be solved in linear time, which generalizes Chen’s result (Discrete Math. 23:1400–1415, 2009) for trees, and the time complexity is much better than the algorithm in Ben-Zwi et al. (Discrete Optim., 2010) (for bounded treewidth graphs) when restricted to block-cactus graphs. We show that if the underlying graph G is a chordal graph with thresholds θ(v)≤2 for each vertex v in G, then the problem can be solved in linear time. For a Hamming graph G having thresholds θ(v)=2 for each vertex v of G, we precisely determine an optimal target set S for (G,θ). These results partially answer an open problem raised by Dreyer and Roberts (Discrete Appl. Math. 157:1615–1627, 2009). 相似文献
Journal of Combinatorial Optimization - The increasingly serious traffic congestion makes the bus system more and more inefficient. It is recognized all over the world that designing an attractive... 相似文献
Journal of Combinatorial Optimization - Recycling of end-of-life (EOL) products has drawn much attention from both researchers and practitioners over the recent decades due to the environmental... 相似文献
Journal of Combinatorial Optimization - In this paper we study the capacitated vehicle routing problem. An instance of capacitated vehicle routing problem consists of a set of vertices with demands... 相似文献
Journal of Combinatorial Optimization - Considering that the time of meeting the demands is very important for emergency vehicle and emergency vehicle can’t reject any request, we introduce a... 相似文献
With the booming development of sharing economy, decision makers must consider the effect when making decisions with uncertain demands. In the leasing problem, people are faced with several leasing options. Participating in the shared leasing option can reduce the cost of the lessee, which makes it a good choice. This paper considers the online leasing option under sharing economy. By applying competitive analysis to the two-option online leasing problem, the optimal competitive ratios of the deterministic and randomized strategies with market interest rate are obtained, respectively. The theoretical results show that the strategies’ competitive performance is improved under sharing economy. Furthermore, numerical examples are performed to illustrate that considering the shared option has a significant influence on the two-option online leasing problem.