Daniel Raible

An exact algorithm for the Maximum Leaf Spanning Tree problem

Given an undirected graph with n vertices, the Maximum Leaf Spanning Tree problem is to find a spanning tree with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4kpoly(n)) using a simple branching algorithm introduced by a subset of the authors (Kneis et al. 2008 16). Daligault et al. (2010) 6 improved the branching and obtained a running time of O(3.72kpoly(n)). In this paper, we study the problem from an exponential time viewpoint, where it is equivalent to the Connected Dominating Set problem. Here, Fomin, Grandoni, and Kratsch showed how to break the ?(2n) barrier and proposed an O(1.9407n)-time algorithm (Fomin et al. 2008 11). Based on some useful properties of Kneis et al. (2008) 16 and Daligault et al. (2010) 6, we present a branching algorithm whose running time of O(1.8966n) has been analyzed using the Measure-and-Conquer technique. Finally, we provide a lower bound of ?(1.4422n) for the worst case running time of our algorithm.

A parameterized perspective on packing paths of length two

AbstractWe study (vertex-disjoint) packings of paths of length two (i.e., of P2’s) in graphs under a parameterized perspective. Starting from a maximal P2-packing ℘ of size j we use extremal combinatorial arguments for determining how many vertices of ℘ appear in some P2-packing of size (j+1) (if such a packing exists). We prove that one can ‘reuse’ 2.5j vertices. We also show that this bound is asymptotically sharp. Based on a WIN-WIN approach, we build an algorithm which decides, given a graph, if a P2-packing of size at least k exists in time

An Exact Algorithm for the Maximum Leaf Spanning Tree Problem

\mathcal{O}^{*}(2.448^{3k})

An Amortized Search Tree Analysis for k-Leaf Spanning Tree

.

Exact and Parameterized Algorithms for Max Internal Spanning Tree

Given an undirected graph G with n nodes, the Maximum Leaf Spanning Tree problem asks to find a spanning tree of G with as many leaves as possible. When parameterized in the number of leaves k, this problem can be solved in time O(4 k poly(n)) using a simple branching algorithm introduced by a subset of the authors [13]. Daligault, Gutin, Kim, and Yeo [6] improved this branching algorithm and obtained a running time of O(3.72 k poly(n)). In this paper, we study the problem from an exact exponential time point of view, where it is equivalent to the Connected Dominating Set problem. For this problem Fomin, Grandoni, and Kratsch showed how to break the ?(2 n ) barrier and proposed an O(1.9407 n ) time algorithm [10]. Based on some properties of [6] and [13], we establish a branching algorithm whose running time of O(1.8966 n ) has been analyzed using the Measure-and-Conquer technique. Finally we provide a lower bound of ?(1.4422 n ) for the worst case running time of our algorithm.

Improved algorithms and complexity results for power domination in graphs

The problem of finding a spanning tree in an undirected graph with a maximum number of leaves is known to be

Searching Trees: An Essay

\mathcal{NP}

A New Upper Bound for Max-2-SAT: A Graph-Theoretic Approach

-hard. We present an algorithm which finds a spanning tree with at least k leaves in time O *(3.4575 k ) which improves the currently best algorithm. The estimation of the running time is done by using a non-standard measure. The present paper is one of the few examples that employ the Measure & Conquer paradigm of algorithm analysis, developed within the field of Exact Exponential-Time Algorithmics, within the area of Parameterized Algorithmics.

Exact algorithms for maximum acyclic subgraph on a superclass of cubic graphs

We consider the

Power Domination in

\mathcal{NP}