Searches on star graphs and equivalent oracle problems

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.022318· OSTI ID:21537134

Lee, Jaehak; Lee, Hai-Woong ^[1]; Hillery, Mark ^[2]

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1. Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701 (Korea, Republic of)
2. Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10021 (United States)

We examine a search on a graph among a number of different kinds of objects (vertices), one of which we want to find. In a standard graph search, all of the vertices are the same, except for one, the marked vertex, and that is the one we wish to find. We examine the case in which the unmarked vertices can be of different types, so the background against which the search is done is not uniform. We find that the search can still be successful, but the probability of success is lower than in the uniform background case, and that probability decreases with the number of types of unmarked vertices. We also show how the graph searches can be rephrased as equivalent oracle problems.

• OSTI ID: 21537134
• Journal Information: Physical Review. A, Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevA.83.022318; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
GRAPH THEORY
PROBABILITY
VERTEX FUNCTIONS
FUNCTIONS
MATHEMATICS