A parameterized perspective on packing paths of length two

Journal of Combinatorial Optimization

Volumn 18, Issue 4, 2009, Pages 319-341

  Fernau, Henning ^a   Raible, Daniel ^a  

^a UNIVERSITY OF TRIER   (Germany)

Author keywords

Extremal combinatorics; Parameterized algorithms; Path packing

Indexed keywords

ALGORITHMS;

EXTREMAL; EXTREMAL COMBINATORICS; PARAMETERIZED; PARAMETERIZED ALGORITHM; PATH PACKINGS; WIN-WIN;

PARAMETERIZATION;

EID: 84897976989     PISSN: 13826905     EISSN: 15732886     Source Type: Journal    
DOI: 10.1007/s10878-009-9230-0     Document Type: Article

References (31)

1. Bazgan C, Hassin R, Monnot J (2005) Approximation algorithms for some vehicle routing problems. Discrete Appl Math 146:27-42
2. De Bontridder KMJ, Halldórsson BV, Halldórsson MM, Lenstra JK, Ravi R, Stougie L (2003) Approximation algorithms for the test cover problem. Math Program, Ser B 98:477-491
3. Chen J, Fernau H, Kanj YA, Xia G (2007) Parametric duality and kernelization: lower bounds and upper bounds on kernel size. SIAM J Comput 37:1077-1108
4. Chen J, Fernau H, Ning D, Raible D, Wang J (2008) A parameterized perspective on P2-packings. Technical report 0804.0570, ArXiv, http://arxiv.org/abs/0804.0570
5. Cotta C, Moscato P (2002) On the parameterized complexity of problems related with feature identification for gene expression data mining techniques. Bioinformatics 1:1-8
6. Cotta C, Moscato P (2003) The k-feature set problem is W[2]-complete. J Comput Syst Sci 67:686-690
7. Dehne F, Fellows M, Fernau H, Prieto E, Rosamond F (2006) NONBLOCKER: parameterized algorithmics for MINIMUM DOMINATING SET. In: Štuller J, Wiedermann J, Tel G, Pokorný J, Bielikova M (eds) Software seminar SOFSEM. LNCS, vol 3831. Springer, Berlin, pp 237-245
8. Downey RG, Fellows MR (1999) Parameterized complexity. Springer, Berlin
9. Estivill-Castro V, Fellows MR, LangstonMA, Rosamond FA (2005) FPT is P-time extremal structure I. In: Broersma H, Johnson M, Szeider S (eds) Algorithms and complexity in Durham ACiD 2005. Texts in algorithmics, vol 4. King's College, London, pp 1-41
10. FellowsM(2002) Parameterized complexity: the main ideas and connections to practical computing. Electron Notes Theor Comput Sci 61
11. Fernau H (2005) Parameterized algorithmics: a graph-theoretic approach. Habilitationsschrift, Universität Tübingen, Germany
12. Fernau H, Manlove DF (2006) Vertex and edge covers with clustering properties: Complexity and algorithms. In: Algorithms and complexity in Durham ACiD 2006. King's College, London, pp 69-84
13. Fernau H, Raible D (2008) A parameterized perspective on packing paths of length two. In: Yang B, Du D-Z, An Wang C (eds) Combinatorial optimization and applications COCOA. LNCS, vol 5165. Springer, Berlin, pp 54-63
14. Gallai T (1959) Über extreme Punkt-und Kantenmengen. Ann Univ Sci Bp Eötvös Sect Math 2:133-138
15. Hassin R, Rubinstein S (1997) An approximation algorithm for maximum packing of 3-edge paths. Inf Process Lett 63:63-67
16. Hassin R, Rubinstein S (2006) An approximation algorithm for maximum triangle packing. Discrete Appl Math 154:971-979; 2620 [Erratum]
17. Hell P, Kirkpatrick DG (1982) Star factors and star packings. Technical report 82-6, Computing Science, Simon Fraser University, Burnaby, BC V5A1S6, Canada
18. Hopcroft JE, Karp RM (1973) An n5/2-algorithm for maximum matchings in bipartite graphs. SIAM J Comput 2(4):225-231
19. Khot S, Raman V (2002) Parameterized complexity of finding subgraphs with hereditary properties. Theor Comput Sci 289:997-1008
20. Kirkpatrick DG, Hell P (1978) On the completeness of a generalized matching problem. In: ACM symposium on theory of computing STOC, pp. 240-245
21. Kosowski A, Malafiejski M, Zyli'nski P (2005) Packing three-vertex paths in a subcubic graph. In: Felsner S (ed) 2005 European conference on combinatorics, graph theory and applications (EuroComb '05). DMTCS proceedings, Discrete mathematics and theoretical computer science, vol AE. Springer, Berlin, pp 213-218
22. Koutis I (2008) Faster algebraic algorithms for path and packing problems. In: Aceto L, Damgård I, Ann Goldberg L, Halldórsson MM, Ingólfsdóttir A, Walukiewicz I (eds) Automata, languages and programming, 35th international colloquium, ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part I: Tack A: algorithms, automata, complexity, and games. Lecture notes in computer science, vol 5125. Springer, Berlin, pp 575-586
23. Liu Y, Lu S, Chen J, Sze S-H (2006) Greedy localization and color-coding: improved matching and packing algorithms. In: Bodlaender HL, LangstonM(eds) International workshop on parameterized and exact computation IWPEC. LNCS, vol 4169. Springer, Berlin, pp 84-95
24. Micali S, Vazirani VV (1980) An O (v |V ||E|) algorithm for finding maximum matchings in general graphs. In: Symposium on foundations of computer science. IEEE Press, New York, pp 17-27
25. Monnot J, Toulouse S (2007) The Pk partitioning problem and related problems in bipartite graphs. In: van Leeuwen J et al (eds) Software seminar SOFSEM 2008. Lecture notes in computer science, vol 4362. Springer, Berlin, pp 422-433
26. Moser H (2009) A problem kernelization for graph packing. In: Nielsen M et al (eds) Software seminar SOFSEM. LNCS, vol 5404. Springer, Berlin, pp 401-412
27. Plesník J (1984) Equivalence between the minimum covering problem and the maximum matching problem. Discrete Math 49:315-317
28. Prieto E, Sloper C (2003) Either/or: Using vertex cover structure in designing FPT-algorithms - the case of k-internal spanning tree. In: Proceedings ofWADS 2003, workshop on algorithms and data structures. LNCS, vol 2748. Springer, Berlin, pp 465-483
29. Prieto E, Sloper C (2004) Looking at the stars. In: Downey R, Fellows M, Dehne F (eds) International workshop on parameterized and exact computation IWPEC 2004. LNCS, vol 3162. Springer, Berlin, pp 138-148
30. Wang J, Feng Q (2008) An O * (3.523k) parameterized algorithm for 3-set packing. In: Agrawal M et al (eds) Theory and applications of models of computation TAMC. LNCS, vol 4978. Springer, Berlin, pp 82-93
31. Wang J, Ning D, Feng Q, Chen J (2008) An improved parameterized algorithm for a generalized matching problem. In: AgrawalMet al (eds) Theory and applications of models of computation TAMC. LNCS, vol 4978. Springer, Berlin, pp 212-222