FPT is P-Time Extremal Structure I

We describe a broad program of research in parameterized complexity, and hows this plays out for the MAX LEAF SPANNING TREE problem.

[1]  Rodney G. Downey,et al.  Parameterized complexity for the skeptic , 2003, 18th IEEE Annual Conference on Computational Complexity, 2003. Proceedings..

[2]  R. Downey,et al.  Parameterized Computational Feasibility , 1995 .

[3]  R. Battiti,et al.  Covering Trains by Stations or the Power of Data Reduction , 1998 .

[4]  Ge Xia,et al.  Simplicity is Beauty: Improved Upper Bounds for Vertex Cover , 2005 .

[5]  Rolf Niedermeier,et al.  Ubiquitous Parameterization - Invitation to Fixed-Parameter Algorithms , 2004, MFCS.

[6]  Gerhard J. Woeginger,et al.  A Faster FPT Algorithm for Finding Spanning Trees with Many Leaves , 2003, MFCS.

[7]  Gerhard J. Woeginger,et al.  Exact Algorithms for NP-Hard Problems: A Survey , 2001, Combinatorial Optimization.

[8]  Michael R. Fellows,et al.  An O(2O(k)n3) FPT Algorithm for the Undirected Feedback Vertex Set Problem , 2005, COCOON.

[9]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[10]  Michael R. Fellows,et al.  Finite-State Computability of Annotations of Strings and Trees , 1996, CPM.

[11]  Paul D. Seymour,et al.  Spanning trees with many leaves , 2001, J. Graph Theory.

[12]  Gerhard J. Woeginger,et al.  Exact (Exponential) Algorithms for the Dominating Set Problem , 2004, WG.

[13]  Michael R. Fellows,et al.  On computing graph minor obstruction sets , 2000, Theor. Comput. Sci..

[14]  Michael R. Fellows,et al.  Blow-Ups, Win/Win's, and Crown Rules: Some New Directions in FPT , 2003, WG.

[15]  Rolf Niedermeier,et al.  A refined search tree technique for Dominating Set on planar graphs , 2005, J. Comput. Syst. Sci..

[16]  Yuri Gurevich,et al.  The challenger-Solver Game: variations on the Theme of P=NP , 2017, Current Trends in Theoretical Computer Science.

[17]  Jörg Flum,et al.  Query evaluation via tree-decompositions , 2001, JACM.

[18]  P. Seymour,et al.  Surveys in combinatorics 1985: Graph minors – a survey , 1985 .

[19]  Christian Sloper,et al.  Looking at the stars , 2004, Theor. Comput. Sci..

[20]  Hans L. Bodlaender,et al.  On Linear Time Minor Tests with Depth-First Search , 1993, J. Algorithms.

[21]  Henning Fernau,et al.  2 Contents , 1996 .

[22]  Karsten Weihe On the Differences between "Practical" and "Applied" , 2000, Algorithm Engineering.

[23]  Martin Grohe,et al.  The parameterized complexity of database queries , 2001, PODS '01.

[24]  Michael R. Fellows,et al.  Coordinatized Kernels and Catalytic Reductions: An Improved FPT Algorithm for Max Leaf Spanning Tree and Other Problems , 2000, FSTTCS.

[25]  Michael R. Fellows,et al.  On Well-Partial-Order Theory and its Application to Combinatorial Problems of VLSI Design , 1989, SIAM J. Discret. Math..

[26]  Leizhen Cai,et al.  Parameterized Complexity of Vertex Colouring , 2003, Discret. Appl. Math..

[27]  Michael R. Fellows,et al.  Finding k Disjoint Triangles in an Arbitrary Graph , 2004, WG.

[28]  Michael R. Fellows,et al.  Linear Kernels in Linear Time, or How to Save k Colors in O(n2) Steps , 2004, WG.

[29]  Bruce A. Reed,et al.  Finding odd cycle transversals , 2004, Oper. Res. Lett..

[30]  R. Ravi,et al.  Approximating Maximum Leaf Spanning Trees in Almost Linear Time , 1998, J. Algorithms.

[31]  Michael R. Fellows,et al.  Finite automata, bounded treewidth, and well-quasiordering , 1991, Graph Structure Theory.

[32]  Jochen Alber,et al.  Exact algorithms for NP hard problems on networks: design, analysis and implementation , 2002 .

[33]  Martin Grohe,et al.  Definability and Descriptive Complexity on Databases of Bounded Tree-Width , 1999, ICDT.

[34]  Michael R. Fellows,et al.  Parameterized complexity: A framework for systematically confronting computational intractability , 1997, Contemporary Trends in Discrete Mathematics.

[35]  Michael R. Fellows,et al.  Parameterized Complexity: The Main Ideas and Connections to Practical Computing , 2000, Experimental Algorithmics.

[36]  Michael R. Fellows,et al.  An analogue of the Myhill-Nerode theorem and its use in computing finite-basis characterizations , 1989, 30th Annual Symposium on Foundations of Computer Science.

[37]  Rolf Niedermeier,et al.  Improved Tree Decomposition Based Algorithms for Domination-like Problems , 2002, LATIN.

[38]  Joseph G. Peters,et al.  Regularity and Locality in K-terminal Graphs , 1994, Discret. Appl. Math..

[39]  Rolf Niedermeier,et al.  Improved Fixed-Parameter Algorithms for Two Feedback Set Problems , 2005, WADS.

[40]  Dimitrios M. Thilikos,et al.  Invitation to fixed-parameter algorithms , 2007, Comput. Sci. Rev..

[41]  Hans L. Bodlaender,et al.  On Linear Time Minor Tests and Depth First Search , 1989, WADS.

[42]  Kurt Mehlhorn,et al.  Graph Algorithm and NP-Completeness , 1984 .

[43]  B. TRUMPY,et al.  University of Bergen , 1948, Nature.

[44]  Rolf Niedermeier,et al.  Refined Search Tree Technique for DOMINATING SET on Planar Graphs , 2001, MFCS.

[45]  Jan Arne Telle,et al.  Practical Algorithms on Partial k-Trees with an Application to Domination-like Problems , 1993, WADS.

[46]  Michael R. Fellows,et al.  Greedy Localization, Iterative Compression, Modeled Crown Reductions: New FPT Techniques, an Improved Algorithm for Set Splitting, and a Novel 2k Kernelization for Vertex Cover , 2004, IWPEC.

[47]  Michael R. Fellows,et al.  Kernelization Algorithms for the Vertex Cover Problem: Theory and Experiments , 2004, ALENEX/ANALC.

[48]  John Michael Robson,et al.  Algorithms for Maximum Independent Sets , 1986, J. Algorithms.

[49]  Elena Prieto Rodríguez,et al.  SYSTEMATIC KERNELIZATION IN FPT ALGORITHM DESIGN , 2005 .