A new view on Rural Postman based on Eulerian Extension and Matching

Journal of Discrete Algorithms

Volumn 16, Issue , 2012, Pages 12-33

  Sorge, Manuel ^a   Van Bevern, René ^a   Niedermeier, Rolf ^a   Weller, Mathias ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Arc addition; Arc routing; Chinese postman; Parameterized complexity

Indexed keywords

ARC ADDITION; ARC ROUTING; ARC ROUTING PROBLEMS; BIPARTITE GRAPHS; CHINESE POSTMAN; EULERIAN; MATCHING PROBLEMS; MULTIGRAPHS; NP-HARD; NP-HARDNESS; PARAMETERIZED; PARAMETERIZED COMPLEXITY; PERFECT MATCHINGS; WEAKLY CONNECTED COMPONENTS;

COMPUTATIONAL METHODS;

COMBINATORIAL MATHEMATICS;

EID: 84865483427     PISSN: 15708667     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jda.2012.04.007     Document Type: Conference Paper

References (35)

1. A.A. Assad, and B.L. Golden Arc routing methods and applications Network Routing Handbooks in Operations Research and Management Science vol. 8 1995 Elsevier B.V. 375 483
2. J. Bang-Jensen, and G. Gutin Digraphs: Theory, Algorithms and Applications second edition 2008 Springer
3. E. Benavent, A. Corberán, E. Piñana, I. Plana, and J.M. Sanchis New heuristic algorithms for the windy rural postman problem Comput. Oper. Res. 32 12 2005 3111 3128
4. F.T. Boesch, C. Suffel, and R. Tindell The spanning subgraphs of Eulerian graphs J. Graph Theory 1 1977 79 84
5. E.A. Cabral, M. Gendreau, G. Ghiani, and G. Laporte Solving the hierarchical Chinese postman problem as a rural postman problem European J. Oper. Res. 155 1 2004 44 50
6. L. Cai, and B. Yang Parameterized complexity of even/odd subgraph problems J. Discrete Algorithms 9 2011 231 240
7. N. Christofides, V. Campos, A. Corberán, and E. Mota An Algorithm for the Rural Postman Problem on a Directed Graph Mathematical Programming Study vol. 26 1986 pp. 155-166
8. A. Corberán, J.M. Sanchis, A polyhedral approach to the rural postman problem, Technical report, Departamento de Estadística e Investigación Operativa, Universidad de Valencia, Spain, 1991.
9. M. Cygan, D. Marx, M. Pilipczuk, M. Pilipczuk, and I. Schlotter Parameterized complexity of Eulerian deletion problems Proc. 37th WG LNCS vol. 6986 2011 Springer 131 142
10. F. Dorn, H. Moser, R. Niedermeier, and M. Weller Efficient algorithms for Eulerian extension Proc. 36th WG LNCS vol. 6410 2010 Springer 100 111 Full version submitted to SIAM Journal on Discrete Mathematics
11. R.G. Downey, and M.R. Fellows Parameterized Complexity 1999 Springer
12. M. Dror Arc Routing: Theory, Solutions, and Applications 2000 Kluwer Academic Publishers
13. J. Edmonds, and E.L. Johnson Matching, Euler tours and the Chinese postman Math. Program. 5 1973 88 124
14. H.A. Eiselt, M. Gendreau, and G. Laporte Arc routing problems, Part II: The rural postman problem Oper. Res. 43 3 1995 399 414
15. J. Flum, and M. Grohe Parameterized Complexity Theory 2006 Springer
16. F.V. Fomin, and P.A. Golovach Parameterized complexity of connected even/odd subgraph problems Proc. 29th STACS, vol. 14 2012 LZI Dagstuhl, Germany 432 440
17. G.N. Frederickson Approximation algorithms for some postman problems J. ACM 26 3 1979 538 554
18. G.N. Frederickson, Approximation algorithms for NP-hard routing problems, PhD thesis, Faculty of the Graduate School of the University of Maryland, 1977.
19. G. Ghiani, and G. Laporte A branch-and-cut algorithm for the undirected rural postman problem Math. Program. 87 2000 467 481
20. G. Groves, and J. Van Vuuren Efficient heuristics for the rural postman problem ORiON 21 1 2005 33 51
21. J. Guo, F. Hüffner, and R. Niedermeier A structural view on parameterizing problems: Distance from triviality Proc. 1st IWPEC LNCS vol. 3162 2004 Springer 162 173
22. W. Höhn, T. Jacobs, and N. Megow On Eulerian extensions and their application to no-wait flowshop scheduling J. Sched. 2011 available electronically
23. J.K. Lenstra, and A.H.G.R. Kan On general routing problems Networks 6 3 1976 273 280
24. L. Lesniak, and O.R. Oellermann An Eulerian exposition J. Graph Theory 10 3 1986 277 297
25. A.N. Letchford, Polyhedral results for some constrained arc-routing problems, PhD thesis, Lancaster University, Lancaster, United Kingdom, 1996.
26. K. Mei-Ko Graphic programming using odd or even points Chinese Math. 1 1962 273 277
27. R. Niedermeier Invitation to Fixed-Parameter Algorithms 2006 Oxford University Press
28. C.S. Orloff A fundamental problem in vehicle routing Networks 4 1 1974 35 64
29. C.S. Orloff On general routing problems: Comments Networks 6 3 1976 281 284
30. M. Pérez-Delgado A solution to the rural postman problem based on artificial ant colonies Current Topics in Artificial Intelligence LNCS vol. 4788 2007 Springer 220 228
31. N. Perrier, A. Langevin, and C.-A. Amaya Vehicle routing for urban snow plowing operations Transp. Sci. 42 1 2008 44 56
32. N. Perrier, A. Langevin, and J.F. Campbell A survey of models and algorithms for winter road maintenance. Part IV: Vehicle routing and fleet sizing for plowing and snow disposal Comput. Oper. Res. 34 1 2007 258 294
33. M. Sorge, On making directed graphs Eulerian, Diplomarbeit, Institut für Informatik, Friedrich-Schiller-Universität Jena, 2011, arXiv:1101.4283 [cs.DM].
34. M. Sorge, R. van Bevern, R. Niedermeier, and M. Weller From few components to an Eulerian graph by adding arcs Proc. 37th WG LNCS vol. 6986 2011 Springer 307 319
35. M. Sorge, R. van Bevern, R. Niedermeier, and M. Weller A new view on rural postman based on Eulerian extension and matching Proc. 22nd IWOCA LNCS vol. 7056 2011 Springer 310 322