Access the full text.
Sign up today, get DeepDyve free for 14 days.
Bernhard Stengel, Ralph Werchner
Discrete Applied Mathematics Complexity of Searching an Immobile Hider in a Graph
P. Hudson (1982)
Search GamesJournal of the Operational Research Society, 33
Ljiljana Pavlović (1995)
A search game on the union of graphs with immobile hiderNaval Research Logistics, 42
S. Alpern, M. Asic (1985)
The search value of a networkNetworks, 15
W. Tutte (1966)
Connectivity in graphs
Joseph Lewin (1994)
Differential Games
S. Alpern, J. Howard (2000)
Alternating Search at Two LocationsDynamics and Control, 10
E. Anderson, M. Aramendía (1990)
The search game on a network with immobile hiderNetworks, 20
Reijnierse Reijnierse, Potters Potters (1993)
Search games with immobile hiderInt J Game Theory, 21
B. Barden, R. Libeskind-Hadas, Janet Davis, William Williams (1999)
On Edge-Disjoint Spanning Trees in HypercubesInf. Process. Lett., 70
A. Beck, Micah Beck (1984)
Son of the linear search problemIsrael Journal of Mathematics, 48
S. Alpern, S. Gal (1988)
A mixed-strategy minimax theorem without compactnessSiam Journal on Control and Optimization, 26
W. Ruckle (1983)
Geometric games and their applications
von Stengel von Stengel, Werchner Werchner (1997)
Complexity of searching an immobile hider in a graphDiscrete Appl Math, 78
S. Gal (2000)
On the optimality of a simple strategy for searching graphsInternational Journal of Game Theory, 29
Arnon Dagan, S. Gal (2008)
Network search games, with arbitrary searcher starting pointNetworks, 52
L. Stone (1975)
Theory of Optimal Search
S. Alpern, S. Gal (2002)
The theory of search games and rendezvous, 55
K. Kikuta (1995)
A SEARCH GAME WITH TRAVELING COST ON A TREEJournal of The Operations Research Society of Japan, 38
(1971)
Edge-disjoint Hamiltonian circuits in graphs with vertices of large valency
S. Alpern (2008)
Hide‐and‐seek games on a tree to which Eulerian networks are attachedNetworks, 52
S. Alpern, V. Baston, S. Gal (2008)
Network search games with immobile hider, without a designated searcher starting pointInternational Journal of Game Theory, 37
H. Eiselt, M. Gendreau, G. Laporte (1994)
ARC ROUTING PROBLEMS.
Eiselt Eiselt, Gendreau Gendreau, Laporte Laporte (1995)
Arc routing problems. I. The Chinese postman problemOper Res, 43
We introduce the notion of a Utilitarian Postman (UP) path on a network Q as one which minimizes the expected time required to find a random (uniformly distributed) point, and show that UP paths must be used in a minimax search of a symmetric network. For any network Q, one may consider the zero‐sum search game Γ(Q) in which the (minimizing) Searcher picks a unit speed path S(t) in Q, the Hider picks a point H in Q, and the payoff is the meeting time T = min{t : S(t) = H}. We show first that if Q is symmetric (edge and vertex transitive), then it is optimal for the Hider to pick H uniformly in Q, so that the Searcher must follow a UP path. We then show that if Q is symmetric of odd degree, with n vertices and m unit length edges, the value V of Γ(Q) satisfies $ V \geq {m \over 2} + {n^{2}-2n \over 8m} $, with equality if and only if (*): Q has a path P = v1, v2,…,vn−1 of distinct vertices, such that the edge set Q′ = Q−∪ i=1(n−2)/2(v2i,v2i+1) is connected. In this case, there is a UP path for Q consisting of P followed by an Eulerian path E of Q′. The condition (*) is satisfied by many symmetric graphs, including all complete graphs, complete bipartite graphs, hypercube graphs, high valency graphs, and the Petersen graph. We know of no odd degree symmetric graph not satisfying (*). © 2009 Wiley Periodicals, Inc. NETWORKS, 2009
Networks: An International Journal – Wiley
Published: Jul 1, 2009
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.