Online Mixed Ring Covering Problem with Two Nodes

Man Xiao (), Weidong Li () and Xiaofei Liu ()
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Man Xiao: Yunnan University
Weidong Li: Yunnan University
Xiaofei Liu: Yunnan University

SN Operations Research Forum, 2023, vol. 4, issue 1, 1-20

Abstract: Abstract In this paper, we study the online mixed ring covering problem, where the ring contains two nodes and undirected and bidirected links. A sequence of flows arrives one by one, where each flow has a traffic demand for each pair of nodes in the ring. The objective is to maximize the minimum load of the ring link, where the load of a link is the total demand of the flows sent to that link. We consider the problem in three different scenarios: splittable, integer splittable and unsplittable. When the demands are splittable, we present an optimal online algorithm with a competitive ratio that is no more than $$\frac{4}{3}$$ 4 3 . When the demands are integer splittable, we present an optimal online algorithm with a competitive ratio that is no more than 2. When the demands are unsplittable, we prove that the lower bound for this case is $$\infty$$ ∞ , and few researchers have provided this result. Then, we consider a special case of the online mixed ring covering problem when the demands are unsplittable, which has a buffer size of K, where K is the number of flows temporarily stored in the buffer. We prove that the competitive ratio for any positive integer K is at least 2. For $$K=1$$ K = 1 , we present an online algorithm with a competitive ratio that is no more than 3. For $$K=2$$ K = 2 , we present an online algorithm with a competitive ratio that is no more than $$\frac{3+\sqrt{5}}{2}\approx 2.618$$ 3 + 5 2 ≈ 2.618 .

Keywords: Mixed ring; Ring covering; Online algorithm; Competitive ratio; Buffer (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s43069-022-00189-x

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