Engineering Tree Labeling Schemes: A Case Study on Least Common Ancestors

Information and Computation

Petreschi

2016

Self Cite

In topology recognition, each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph, with all ports correctly marked. This task is usually unfeasible without any a priori information. Such information can be provided to nodes as advice. An oracle knowing the network can give a (possibly different) string of bits to each node, and all nodes must reconstruct the network using this advice, after a given number of rounds of communication. During each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations. The time of completing topology recognition is the number of rounds it takes, and the size of advice is the maximum length of a string given to nodes.We investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes. We provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time, in the class of all graphs of size n and diameter D ≤ αn, for any constant α < 1. In most cases, our bounds are asymptotically tight.

Section: Related Workmentioning

confidence: 99%

Topology recognition with advice

Fusco

Information and Computation

Petreschi

2016

Self Cite

“…Following the paradigm of algorithms with advice [1,14,16,21,26,28,29,30,31,32,33,34,36,37,38,44,49], this information is provided to the agents at the start of their navigation by an oracle that knows the network, the starting positions of the agents and, in the case of treasure hunt, the node where the treasure is hidden. The oracle assists the agents by providing them with a binary string called advice, which can be used by the agent during the algorithm execution.…”

Section: Model and Problemsmentioning

confidence: 99%

“…Providing nodes or agents with information of arbitrary type that can be used to perform network tasks more efficiently has been proposed in [1,14,16,21,26,28,29,30,31,32,33,34,36,37,38,42,44,49]. This approach was referred to as algorithms with advice.…”

Section: Related Workmentioning

confidence: 99%

Tradeoffs between cost and information for rendezvous and treasure hunt

Miller

Journal of Parallel and Distributed Computing

2015

“…In this paper, we study tradeoffs between the amount of information available a priori to the agents and the cost of rendezvous and treasure hunt. Following the paradigm of algorithms with advice [1,14,16,21,26,28,29,30,31,32,33,34,36,37,38,44,49], this information is provided to the agents at the start of their navigation by an oracle that knows the network, the starting positions of the agents and, in the case of treasure hunt, the node where the treasure is hidden. The oracle assists the agents by providing them with a binary string called advice, which can be used by the agent during the algorithm execution.…”

Section: Model and Problemsmentioning

confidence: 99%

Tradeoffs between Cost and Information for Rendezvous and Treasure Hunt

Miller

Lecture Notes in Computer Science

2014

In rendezvous, two agents traverse network edges in synchronous rounds and have to meet at some node. In treasure hunt, a single agent has to find a stationary target situated at an unknown node of the network. We study tradeoffs between the amount of information (advice) available a priori to the agents and the cost (number of edge traversals) of rendezvous and treasure hunt. Our goal is to find the smallest size of advice which enables the agents to solve these tasks at some cost C in a network with e edges. This size turns out to depend on the initial distance D and on the ratio e C , which is the relative cost gain due to advice. For arbitrary graphs, we give upper and lower bounds of O(D log(D · e C ) + log log e) and Ω(D log e C ), respectively, on the optimal size of advice. For the class of trees, we give nearly tight upper and lower bounds of O(D log e C + log log e) and Ω(D log e C ), respectively.