This chapter surveys early studies and recent developments in the broad area of analysis and design of robust network clusters with bounded diameter. Low diameter (small number of intermediaries in the shortest path between any two nodes) is a desired property of various infrastructure networks (communication/information exchange, transportation/supply, etc.) However, in addition to low diameter, a network cluster may need to be able to withstand multiple disruptions or failures of their elements (nodes and/or links), which is not always a guaranteed property for networks with low diameter. We review mathematical modeling and optimization aspects of studying network clusters with bounded diameter, including basic models (referred to as k-clique and k-club), as well as generalized models with improved failure/attack tolerance characteristics (i.e., R-robust k-club).
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 email@example.com
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 firstname.lastname@example.org