Saket Saurabh

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In a parameterized problem, every instance <i>I</i> comes with a positive integer <i>k</i>. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance <i>I</i> to a polynomial in <i>k</i> while preserving the answer. In this work, we give two meta-theorems on kernelization. The first theorem says that(More)
We obtain a number of lower bounds on the running time of algorithms solving problems on graphs of bounded treewidth. We prove the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi. In particular, assuming that SAT cannot be solved in (2 - &#8712;)<sup><i>n</i></sup><i>m</i><sup><i>O</i>(1)</sup> time, we show that for any(More)
Let M = (E, I) be a matroid and let S = {S1, . . . , St} be a family of subsets of E of size p. A subfamily Ŝ ⊆ S is q-representative for S if for every set Y ⊆ E of size at most q, if there is a set X ∈ S disjoint from Y with X ∪ Y ∈ I, then there is a set X̂ ∈ Ŝ disjoint from Y with X̂ ∪ Y ∈ I. By the classical result of Bollobás, in a uniform matroid,(More)
Bidimensionality theory appears to be a powerful framework in the development of meta-algorithmic techniques. It was introduced by Demaine et al. [<i>J. ACM 2005</i>] as a tool to obtain sub-exponential time parameterized algorithms for bidimensional problems on <i>H</i>-minor free graphs. Demaine and Hajiaghayi [<i>SODA 2005</i>] extended the theory to(More)
We present a randomized subexponential time, polynomial space parameterized algorithm for the k-Weighted Feedback Arc Set in Tournaments (k-FAST) problem. We also show that our algorithm can be derandomized by slightly increasing the running time. To derandomize our algorithm we construct a new kind of universal hash functions, that we coin universal(More)
A central problem in parameterized algorithms is to obtain algorithms with running time <i>f</i>(<i>k</i>) &#183; <i>n</i><sup><i>O</i>(1)</sup> such that <i>f</i> is as slow growing function of the parameter <i>k</i> as possible. In particular, the first natural goal is to make <i>f</i>(<i>k</i>) single-exponential, that is, <i>c</i><sup><i>k</i></sup> for(More)
We investigate the parameterized complexity of <scp>Vertex Cover</scp> parameterized by the difference between the size of the optimal solution and the value of the linear programming (LP) relaxation of the problem. By carefully analyzing the change in the LP value in the branching steps, we argue that combining previously known preprocessing rules with the(More)
The <i>k</i>-Leaf Out-Branching problem is to find an out-branching, that is a rooted oriented spanning tree, with at least <i>k</i> leaves in a given digraph. The problem has recently received much attention from the viewpoint of parameterized algorithms. Here, we take a kernelization based approach to the <i>k</i>-Leaf-Out-Branching problem. We give the(More)