Competitive Maintenance of Minimum Spanning Trees in Dynamic Graphs

Abstract. We consider the online MST and TSP problems with recourse. The nodes of an unknown graph with metric edge cost appear one by one and must be connected in such a way that the resulting tree or tour has low cost. In the standard online setting, with irrevocable decisions, no algorithm can guarantee a constant competitive ratio. In our model we allow recourse actions by giving a limited budget of edge rearrangements per iteration. It has been an open question for more than 20 years if an online algorithm equipped with a constant (amortized) budget can guarantee constant-approximate solutions [7].As our main result, we answer this question affirmatively in an amortized setting. We introduce an algorithm that maintains a nearly optimal tree when given constant amortized budget. In the non-amortized setting, we specify a promising proof technique and conjecture a structural property of optimal solutions that would prove a constant competitive ratio with a single recourse action. It might seem rather optimistic that such a small budget should be sufficient for a significant cost improvement. However, we can prove such power of recourse in the offline setting in which the sequence of node arrivals is known. Even this problem prohibits constant approximations if there is no recourse allowed. Surprisingly, already a smallest recourse budget significantly improves the performance guarantee from non-constant to constant.Unlike in classical TSP variants, the standard double-tree and shortcutting approach does not give constant guarantees in the online setting. However, a non-trivial robust shortcutting technique allows to translate online MST results into TSP results at the loss of small factors.

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“…A related online MST variant has been studied in [6]. Here, in each iteration the cost of some edge increases or decreases by one.…”

Section: Introductionmentioning

confidence: 99%

The Power of Recourse for Online MST and TSP

Megow

Skutella

Verschae

et al. 2012

Automata, Languages, and Programming

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“…We believe that automatic adjustments of a spanning tree based on the ping times between agents in a cluster (which is a case of an online minimum weighted spanning tree problem [54,31]) can be implemented and we speculate that it can be moderately effective for detecting the actual physical structure of the network for small networks, if proper statistics of ping measurements are used to determine the weights of edges in the graph. While this is a research topic in its own right, and is out of scope of the current system prototype, we plan to experiment with this approach in the future.…”

Section: Broadcasting Through the Spanning Treementioning

confidence: 99%

Implementing an eXAT-based distributed monitoring system prototype

et al. 2012

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Monitoring resource utilization in distributed systems remains of importance. This is especially the case in LAN-based distributed systems (and, in particular, in global Grid systems), where individual nodes can be (may need to be) added to and/or removed from the system at ?random? moments. The aim of this paper is to report initial results of the project that aims at using Erlang-based software agents as a robust and flexible resource monitoring infrastructure. The implemented prototype is capable not only of collecting performance data, but can also detect certain network problems. Furthermore, an assessment of the eXAT agent platform, based on experiences gathered during prototype implementation, is included.

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Minimum Spanning Tree in Cognitive Radio Networks: A Distributed Approach to Maintain for Node Failures

Stanzin

Murmu

2018

2018 9th International Conference on Computing, Communication and Networking Technologies (ICCCNT)

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Competitive Maintenance of Minimum Spanning Trees in Dynamic Graphs

Cited by 5 publications

References 12 publications

The Power of Recourse for Online MST and TSP

The Power of Recourse for Online MST and TSP

Implementing an eXAT-based distributed monitoring system prototype

Minimum Spanning Tree in Cognitive Radio Networks: A Distributed Approach to Maintain for Node Failures

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