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- Fedor V. Fomin, Serge Gaspers, Saket Saurabh, Alexey A. Stepanov
- Algorithmica
- 2009

Branch & Reduce and dynamic programming on graphs of bounded treewidth are among the most common and powerful techniques used in the design of moderately exponential time exact algorithms for NP hard problems. In this paper we discuss the efficiency of simple algorithms based on combinations of these techniques. The idea behind these algorithms is very… (More)

- Daniel Lokshtanov, N. S. Narayanaswamy, Venkatesh Raman, M. S. Ramanujan, Saket Saurabh
- ACM Trans. Algorithms
- 2014

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)

- Michael R. Fellows, Jiong Guo, Dániel Marx, Saket Saurabh
- Dagstuhl Reports
- 2012

- Daniel Lokshtanov, Dániel Marx, Saket Saurabh
- SODA
- 2011

A central problem in parameterized algorithms is to obtain algorithms with running time <i>f</i>(<i>k</i>) · <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)

- Marek Cygan, Fedor V. Fomin, +5 authors Saket Saurabh
- 2015

- Daniel Lokshtanov, Dániel Marx, Saket Saurabh
- SODA
- 2011

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 - ∈)<sup><i>n</i></sup><i>m</i><sup><i>O</i>(1)</sup> time, we show that for any… (More)

- Fedor V. Fomin, Daniel Lokshtanov, Saket Saurabh
- SODA
- 2014

Let M = (E, I) be a matroid and let S = {S 1 ,. .. , S t } be a family of subsets of E of size p. A subfamily S ⊆ 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 X ∈ S disjoint from Y with X ∪ Y ∈ I. By the classical result of Bollobás, in a uniform matroid,… (More)

- Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh
- ICALP
- 2015

In the Subset Feedback Vertex Set (Subset FVS) problem, the input is a graph G on n vertices and m edges, a subset of vertices T , referred to as terminals, and an integer k. The objective is to determine whether there exists a set of at most k vertices intersecting every cycle that contains a terminal. The study of parameterized algorithms for this… (More)

- Fedor V. Fomin, Serge Gaspers, Saket Saurabh
- COCOON
- 2007

We introduce a generic algorithmic technique and apply it on decision and counting versions of graph coloring. Our approach is based on the following idea: either a graph has nice (from the algorithmic point of view) properties which allow a simple recursive procedure to find the solution fast, or the pathwidth of the graph is small, which in turn can be… (More)

- Michael Dom, Daniel Lokshtanov, Saket Saurabh
- ICALP
- 2009

In parameterized complexity each problem instance comes with a parameter k, and a parameterized problem is said to admit a polynomial kernel if there are polynomial time preprocessing rules that reduce the input instance to an instance with size polynomial in k. Many problems have been shown to admit polynomial kernels, but it is only recently that a… (More)