http://nova.newcastle.edu.au/vital/access/services/Feed ${session.getAttribute("locale")} 5 http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:12243 The Convex Recoloring (CR) problem measures how far a tree of characters differs from exhibiting a so-called “perfect phylogeny”. For an input consisting of a vertex-colored tree T, the problem is to determine whether recoloring at most k vertices can achieve a convex coloring, meaning by this a coloring where each color class induces a subtree. The problem was introduced by Moran and Snir (J. Comput. Syst. Sci. 73:1078–1089, 2007; J. Comput. Syst. Sci. 74:850–869, 2008) who showed that CR is NP-hard, and described a search-tree based FPT algorithm with a running time of O(k(k/logk)^k n ⁴). The Moran and Snir result did not provide any nontrivial kernelization. In this paper, we show that CR has a kernel of size O(k²). 2012-12-17T01:00:05.909Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:9494 Therapies consisting of a combination of agents are an attractive proposition, especially in the context of diseases such as cancer, which can manifest with a variety of tumor types in a single case. However uncovering usable drug combinations is expensive both financially and temporally. By employing computational methods to identify candidate combinations with a greater likelihood of success we can avoid these problems, even when the amount of data is prohibitively large. HITTING SET is a combinatorial problem that has useful application across many fields, however as it is NP-complete it is traditionally considered hard to solve exactly. We introduce a more general version of the problem (a,β,d)-HITTING SET, which allows more precise control over how and what the hitting set targets. Employing the framework of Parameterized Complexity we show that despite being NP-complete, the (α,β,d)-HITTING SET problem is fixed-parameter tractable with a kernel of size O(αdkd ) when we parameterize by the size k of the hitting set and the maximum number α of the minimum number of hits, and taking the maximum degree d of the target sets as a constant. We demonstrate the application of this problem to multiple drug selection for cancer therapy, showing the flexibility of the problem in tailoring such drug sets. The fixed-parameter tractability result indicates that for low values of the parameters the problem can be solved quickly using exact methods. We also demonstrate that the problem is indeed practical, with computation times on the order of 5 seconds, as compared to previous Hitting Set applications using the same dataset which exhibited times on the order of 1 day, even with relatively relaxed notions for what constitutes a low value for the parameters. Furthermore the existence of a kernelization for (α,β,d)- HITTING SET indicates that the problem is readily scalable to large datasets. 2012-01-30T05:11:57.782Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:7825 In the framework of parameterized complexity, exploring how one parameter affects the complexity of a different parameterized (or unparameterized problem) is of general interest. A well-developed example is the investigation of how the parameter treewidth influences the complexity of (other) graph problems. The reason why such investigations are of general interest is that real-world input distributions for computational problems often inherit structure from the natural computational processes that produce the problem instances (not necessarily in obvious, or wellunderstood ways). The max leaf number ml(G) of a connected graph G is the maximum number of leaves in a spanning tree for G. Exploring questions analogous to the well-studied case of treewidth, we can ask: how hard is it to solve 3-COLORING, HAMILTON PATH, MINIMUM DOMINATING SET, MINIMUM BANDWIDTH or many other problems, for graphs of bounded max leaf number? What optimization problems are W[1]-hard under this parameterization? We do two things: (1) We describe much improved FPT algorithms for a large number of graph problems, for input graphs G for which ml(G) ≤ k, based on the polynomial-time extremal structure theory canonically associated to this parameter. We consider improved algorithms both from the point of view of kernelization bounds, and in terms of improved fixed-parameter tractable (FPT) runtimes O*(f (k)). (2) The way that we obtain these concrete algorithmic results is general and systematic. We describe the approach, and raise programmatic questions. 2011-06-02T06:00:26.725Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:7412 Kernelization is a strong and widely-applied technique in parameterized complexity. A kernelization algorithm, or simply a kernel, is a polynomial-time transformation that transforms any given parameterized instance to an equivalent instance of the same problem, with size and parameter bounded by a function of the parameter in the input. A kernel is polynomial if the size and parameter of the output are polynomially-bounded by the parameter of the input. In this paper we develop a framework which allows showing that a wide range of FPT problems do not have polynomial kernels. Our evidence relies on hypothesis made in the classical world (i.e. non-parametric complexity), and revolves around a new type of algorithm for classical decision problems, called a distillation algorithm, which is of independent interest. Using the notion of distillation algorithms, we develop a generic lower-bound engine that allows us to show that a variety of FPT problems, fulfilling certain criteria, cannot have polynomial kernels unless the polynomial hierarchy collapses. These problems include k-Path, k-Cycle, k-Exact Cycle, k-Short Cheap Tour, k-Graph Minor Order Test, k-Cutwidth, k-Search Number, k-Pathwidth, k-Treewidth, k-Branchwidth, and several optimization problems parameterized by treewidth and other structural parameters. 2011-03-16T05:20:05.958Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:153 We develop new techniques to derive lower bounds on the kernel size for certain parameterized problems. For example, we show that unless P = NP, PLANAR VERTEX COVER does not have a problem kernel of size smaller than 4k/3, and PLANAR INDEPENDENT SET and PLANAR DOMINATING SET do not have kernels of size smaller than 2k. We derive an upper bound of 67k on the problem kernel for PLANAR DOMINATING SET improving the previous 335k upper bound by Alber et al. 2010-04-27T05:56:38.866Z ]]> http://nova.newcastle.edu.au/vital/access/manager/Repository/uon:5974 Kernelization is a central technique used in parameterized algorithms, and in other approaches for coping with NP-hard problems. In this paper, we introduce a new method which allows us to show that many problems do not have polynomial size kernels under reasonable complexity-theoretic assumptions. These problems include k-Path, k-Cycle, k-Exact Cycle, k-Short Cheap Tour, k-Graph Minor Order Test, k-Cutwidth, k-Search Number, k-Pathwidth, k-Treewidth, k-Branchwidth, and several optimization problems parameterized by treewidth or cliquewidth. 2010-04-27T04:42:20.971Z ]]>