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The proble-m of path planning is studied for the case of a mobile robot moving in m environment filled with obstpcles whose shape and positions are not known. Under the accewd model, the automaton Munuscript received January 25,1985; revised March 26, 1986 and June 2, 1986. This paper is based on a prior submission o f July 18, 1984. V. J. Lumelsky is with… (More)

- Fedor V. Fomin, Serge Gaspers, Saket Saurabh, Alexey A. Stepanov
- Algorithmica
- 2007

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)

- Fedor V. Fomin, Fabrizio Grandoni, Artem V. Pyatkin, Alexey A. Stepanov
- ACM Trans. Algorithms
- 2008

We provide an algorithm listing all minimal dominating sets of a graph on <i>n</i> vertices in time <i>O</i>(1.7159<sup><i>n</i></sup>). This result can be seen as an algorithmic proof of the fact that the number of minimal dominating sets in a graph on <i>n</i> vertices is at most 1.7159<sup><i>n</i></sup>, thus improving on the trivial… (More)

We show that the number of minimal dominating sets in a graph on n vertices is at most 1.7697, thus improving on the trivial O(2n/√n) bound. Our result makes use of the measure and conquer technique from exact algorithms, and can be easily turned into an O(1.7697) listing algorithm. Based on this result, we derive an O(2.8805n) algorithm for the domatic… (More)

- Frederic Dorn, Joanna Bauer, +19 authors Eelko Penninkx
- 2007

In this thesis we focus on subexponential algorithms for NP-hard graph problems: exact and parameterized algorithms that have a truly subexponential running time behavior. For input instances of size n we study exact algorithms with running time 2 √ n) and parameterized algorithms with running time 2 √ k) ·nO(1) with parameter k, respectively. We study a… (More)

- Serge Gaspers, Saket Saurabh, Alexey A. Stepanov
- TAMC
- 2008

We consider the well studied Full Degree Spanning Tree problem, a NP-complete variant of the Spanning Tree problem, in the realm of moderately exponential time exact algorithms. In this problem, given a graph G, the objective is to find a spanning tree T of G which maximizes the number of vertices that have the same degree in T as in G. This problem is… (More)

- Fedor V. Fomin, Alexey A. Stepanov
- COCOON
- 2007

We show how to count all minimumweighted dominating sets of a graph on n vertices in timeO(1.5535).

We are considering the NP-hard problem of finding a spanning tree with many internal vertices. This problem is a generalization of the famous and well-studied Hamiltonian Path problem. We present an dynamic-programming approach for general and degree-bounded graphs obtaining a run times of the form O∗(cn) (c ≤ 3). The main result is an algorithm for the… (More)

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)

- O A Kostin, S V Rebrikov, A I Ovchinnikov, A A Stepanov, Kh P Takhchidi
- Vestnik oftalmologii
- 2017

AIM
to evaluate functional results of reoperation performed according to the CIRCLE technology and using the VisuMax femtosecond laser and MEL-80 excimer laser in cases of regression of the refractive effect after SMILE surgery.
MATERIAL AND METHODS
We studied a group of post-SMILE patients. In those, who showed regression of the refractive effect at 1… (More)