Abstract
This paper is devoted to a new problem of combinatorial optimization. The problem is called Maximum Weight Archipelago Subgraph Problem (MWASP). Archipelago is a signed graph such that the negative edges connect the components of the graph of the positive edges. The new problem is to find a subset of edges in a weighted signed graph such that (i) if the edges of the subset are deleted from the graph then the remaining graph is an archipelago; and (ii) the subset has minimal total weight among the subsets having property (i). The problem is NP-complete, however a polynomial algorithm is provided to obtain the maximal weight of an edge what is still necessary to delete. The problem MWAP is used to analyze the relation of the blue chips of the Dow Jones Index.
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Peter L. Hammer is the late founding director of RUTCOR. This research started in 1999 when the three other authors visited RUTCOR.
The results of this paper have been presented on the European operations research conference EURO XXIV in Lisbon in 2010 in section MC29 participated by both the third and fourth authors. Bruno Simeone died in October 2010.
Appendix: The blue chips of the Dow Jones industrial average
Appendix: The blue chips of the Dow Jones industrial average
The list below shows the list of the 30 blue chips of DJIA in the period March 17, 1997 to October 31, 1999. Since that time, the system of the stocks in DJIA has been changed several times. The names of some companies have also been changed, ptand as a consequence, some abbreviations are changed, too.
AA | Aluminum Comp. of America | IP | International Paper Company |
ALD | AlliedSignal Incorporated | JNJ | Johnson & Johnson |
AXP | American Express | JPM | JPMorgan Chase |
BA | Boeing | KO | Coca-Cola |
C | Citigroup | MCD | McDonald’s Corporation |
CAT | Caterpillar | MMM | 3M, Minnesota Mining and Manufacturing |
CHV | Chevron | MO | Philip Morris |
DD | DuPont | MRK | Merck & Company, Inc. |
DIS | Walt Disney | PG | Procter & Gamble Company |
EK | Eastman Kodak Company | S | Sears Roebuck & Company |
GE | General Electric | T | AT&T |
GM | General Motors | UK | Union Carbide |
GT | Goodyear | UTX | United Technologies Corporation |
HWP | Hewlett-Packard | WMT | Wal-Mart |
IBM | IBM | XON | EXXON |
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Hammer, P.L., Majlender, P., Simeone, B. et al. Maximum weight archipelago subgraph problem. Ann Oper Res 217, 253–262 (2014). https://doi.org/10.1007/s10479-013-1518-x
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DOI: https://doi.org/10.1007/s10479-013-1518-x