Path-search in the pyramid and in other graphs

Details Path-search in the pyramid and in other graphs Path-search in the pyramid and in other graphs

2011-04-27

arxiv.org/abs/1104.5098v1

Mathematics

Combinatorics

Scientific paper

We are given an acyclic directed graph with one source, and a subset of its edges which contains exactly one outgoing edge for every non-sink vertex. These edges determine a unique path from the source to a sink. We can think of it as a switch in every vertex, which determines which way the water arriving to that vertex flows further. We are interested in determining either the sink the flow arrives, or the whole path, with as few questions as possible. The questions we can ask correspond to the vertices of the graph, and the answer describes the switch, i.e. tells which outgoing edge is in our given subset. Originally the problem was proposed by Soren Riis (who posed the question for pyramid graphs) in the following more general form. We are given a natural number k, and k questions can be asked in a round. The goal is to minimize the number of rounds. We completely solve this problem for complete t-ary trees. Also, for pyramid graphs we present some non-trivial partial results.

Affiliated with

Also associated with

No associations

Rating

Path-search in the pyramid and in other graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Path-search in the pyramid and in other graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Path-search in the pyramid and in other graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-475374