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Parameterized Complexity News Parameterized Complexity News The Newsletter of the Parameterized Complexity Community Volume 4, April 2009 Welcome fpt.wikidot.com and mrfellows.net Frances Rosamond, Editor Parameterized complexity has a WIKI!! The establish- Welcome to the latest issue of the Parameterized Com- ment of the wiki is largely due to Philip, student of plexity Newsletter. Our aim is to be provocative and Venkatesh Raman at IMSc, Chennai who searched for a informative, suggesting new problems while keeping the site that will accept LaTEX. We appreciate Philip for an community abreast of the rapidly expanding list of appli- outstanding job. A wiki is a community forum for sharing cations and techniques. The world records of FPT races news and ideas. It works just like wikipedia, although its (as we know them) are summarized. The newsletter pub- “skin” is a little different (the appearance is changable). lishes exercises for classes, as well as new research ideas. Anyone can add or edit. Enjoy and please help keep it There have been an increasing number of parameter- up to date. ized complexity papers presented at conferences this past Philip has also helped create a website for Mike. He year. We are all proud of the smart researchers doing has written a program to fill in the Bibtex and the lengthy such excellent work and I have tried to list some of them process of detailing all Mike’s papers is underway. But, in this newsletter. I apologize for those missed. Some it is quite a job. Mike has over 2000 citations (that non-parameterized papers have also probably been listed. are not self-citations by himself or co-authors) and over Contributions or requests may be sent to my email ad- 1000 are in the past 4 years. The “mrfellows.net” stands dress: ([email protected]). Suggestions for a newslet- for “Michael Ralph”. Note that Mike’s email address is ter logo are welcome. The newsletter is archived at [email protected]. the IWPEC website, (http://www.scs.carleton.ca/ ~dehne/iwpec) and at the new FPT wiki. Some New Developments Gold Ring Project By Saket Saurabh ([email protected]) Independent Odd Cycle Transversal: In the In- The FPT Newsletter invites all the subprograms in the dependent Odd Cycle Transversal problem, we are Computer Journal Special Issue and others, to list the given as input a graph G =(V,E) and a positive integer most important problems waiting to be solved. The k and the question is whether there exists a set I ⊆ V Newsletter and wiki is willing to be a Central Clear- of size at most k such that I is an independent set and ing House. A “special ceremony” at IWPEC will induct G[V \ I] is bipartite. The parameterized complexity of members into the Gadgeteers Club. this problem has been open for some years now. Marx, Sullivan and Razgon have settled this open problem in affirmative by obtaining a fixed parameter tractable al- gorithm for Independent Odd Cycle Transversal. In fact they present a method for reducing the treewidth Contents of this issue: PC and Artificial Intelligence . 2 Welcome........................................1 SocialChoice............................. 3 GoldRingProject...............................1 Established FPT Races. .5 fpt.wikidot.com and mrfellows.net .. 1 SpecialIssue...............................6 Some New Developments . 1 NewDissertations.........................6 SteinerTree:..............................2 Conferences...............................6 Kernelization for Dominating Set: . 2 Positions Advertised . 10 Kernelization Lower Bounds: . 2 Parameterized Complexity News 2 of a graph while preserving all the minimal s − t sep- Kernelization Lower Bounds: Many problems arators. This technique seems very useful in designing have been shown to admit polynomial kernels, but it parameterized algorithms for cut problems. The relevant is only recently that a framework for showing the non- literature can be found here. existence of polynomial kernels for specific problems has been developed by Bodlaender et al. [ICALP, 2008] and • D´aniel Marx, Barry O’Sullivan and Igor Raz- Fortnow and Santhanam [STOC, 2008]. These two semi- gon, Treewidth reduction for constrained separation nal papers have led the foundation of kernelizationn lower and bipartization problems, CoRR abs/0902.3780 bounds. With few exceptions, all known kernelization (2009). lower bounds results have been obtained by directly ap- plying this framework. Recently, there has been a lot Steiner Tree: It is well known that Steiner Tree of progress in this direction. Bodlaender, Thomass´e,and parameterized by the number of terminals can be solved Yeo introduced the notion of polynomial parameter trans- in time O(3knO(1)) using the famous Dreyfus-Wagner al- formations and combined this with non-trivial composi- gorithm. In a breakthrough result Koivisto et al.[STOC, tion algorithm and showed that the Disjoint Paths and 2007] obtained an algorithm running in time and space Disjoint Cycles problems do not admit a polynomial k O(1) 3 O(2 n ) using fast subset convolution. Continuing this kernel unless PH =Σp. In another result of this type, line of research Jesper gives an algorithm running in time Dom, Lokshtanov and Saurabh introduced a notion of col- O(2knO(1)) and using polynomial space. He introduced ors and ids and used it to show that Connected Vertex the concept of branching walks, and obtains the algo- Cover, Capacitated Vertex Cover, Steiner Tree, rithm by extending the inclusion exclusion algorithm of Unique Coverage and various other natural parame- Karp with branching walks. The article containing this terized problems do not admit a polynomial kernel unless 3 result can be found here. PH =Σp. • Jesper Nederlof, Fast polynomial-space algorithms • Hans L. Bodlaender, St´ephanThomass´e,and An- using Mobius inversion: Improving on Steiner Tree ders Yeo, Analysis of Data Reduction: Transforma- and related problems, (2009). Available from home- tions give evidence for non-existence of polynomial page. kernels (2009). Kernelization for Dominating Set: Dominating • Michael Dom, Daniel Lokshtanov, and Saket Set has been a test-bed for making subexponential time Saurabh: Incompressibility through Colors and IDs algorithms and linear kernelization on planar graphs. The (2009). seminal result of Alber et al. [JACM, 2004] obtaining a linear kernel for Dominating Set has been used as a template in obatining linear kernels for various prob- PC and Artificial Intelligence lems on planar graphs. This result was later extended to graphs of bounded genus by Fomin and Thilikos [ICALP, Probabilistic Analysis of Data Reduction and In- 2004]. Recently, Alon and Gutner extended this result tractable Parameterized Problems and obtained a kernel of size kc in graphs excluding a By Yong Gao ([email protected]), University of fixed graph H as a minor, where c only depends on |H|. British Columbia Okanagan, Canada. Data reduction is Alon and Gutner leave as an open problem whether one a key technique in designing efficient algorithms for fixed can obtain a polynomial kernel for Dominating Set in parameter tractable problem and exact exponential-time d-degenerate graphs. Philip, Raman, and Sikdar settled algorithms for NP-hard problems. In the artificial intelli- this open problem by obtaining a polynomial kernel in gence literature, pruning techniques based on simple and graphs excluding Ki,j as a subgraph. Observe that d- efficient-to-implement reduction rules also play a crucial degenerate graph does not have Kd+1,d+1 as a subgraph. role in the success of many industrial-strength solvers, most notably in satisfiability testing, constraint process- • Noga Alon and Shai Gutner, Kernels for the domi- ing, and heuristic state space search. nating set problem on graphs with an excluded mi- In artificial intelligence and theoretical computer sci- nor, ECCC Report TR08-066 ence, the continued interest over the past more than ten • Geevarghese Philip, Venkatesh Raman, and Som- nath Sikdar, Polynomial Kernels for Dominating Set in Ki,j -free and d-degenerate Graphs, (2009). Parameterized Complexity News 3 years in the phase transition phenomenon of random in- presently uses PageRank, but faster and better algo- stances of NP-complete problems is largely motivated by rithms are needed. Similar ranking algorithms may play the expectation that such study will help shed lights on a role in evaluating microarray datasets in bioinformatics, why simple heuristics work on typical problem instances determining how to combine gene expression information and in what situations. with network structure derived from gene ontologies or Yong Gao (University of British Columbia Okana- expression profile correlations. gan, Canada) has recently started an effort to extend Algorithms for merging preference aggregation are this line of research to intractable parameterized prob- needed in multi-agent intelligent systems such as com- lems. He is currently focusing on random instances of puterised air-traffic control where systems from neigh- the Weighted d-CNF Satisfiability problem (Weighted d- bouring countries may negotiate between themselves to SAT) generated under a variety of reasonable random track flights and recommend available runways, and in models. A recently-obtained result shows that an algo- Learning Theory where consensus by motion sensors may rithm based on data reduction techniques is able to solve help train robots to maintain balance. Arkadii Slinko a typical instance of Weighted d-SAT in fixed-parameter (U. Auckland) is investigating how to create autonomous time O(dknd) where n is the number of variables and k software agents capable of acting as group members and is the usual parameter in weighted SAT. This seems to participating in group decision making [10, 11]. be the first in the literature that provides a sound the- With funding by the German Research Agency, Detlef oretical evidence on the power of simple data reductions Seese (Uni Karlsruhe) is investigating trading strategies, for intractable parameterized problems and on the fixed- auctions (eBay.de), and intelligent systems in manage- parameter tractability of random instances of intractable ment of risk and complexity.
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