Édouard Bonnet

On Subexponential and FPT-Time Inapproximability

Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithm design. While each of them being very active in its own, there is an increasing attention to the connection between these different frameworks. In particular, whether Independent Set would be better approximable once endowed with subexponential-time or FPT-time is a central question. In this article, we provide new insights to this question using two complementary approaches; the former makes a strong link between the linear PCP conjecture and inapproximability; the latter builds a class of equivalent problems under approximation in subexponential time.

Multi-parameter Complexity Analysis for Constrained Size Graph Problems: Using Greediness for Parameterization

We study the parameterized complexity of a broad class of problems called “local graph partitioning problems” that includes the classical fixed cardinality problems as max k -vertex cover, k -densest subgraph, etc. By developing a technique that we call “greediness-for-parameterization”, we obtain fixed parameter algorithms with respect to a pair of parameters k, the size of the solution (but not its value) and \(\varDelta\), the maximum degree of the input graph. In particular, greediness-for-parameterization improves asymptotic running times for these problems upon random separation (that is a special case of color coding) and is more intuitive and simple. Then, we show how these results can be easily extended for getting standard-parameterization results (i.e., with parameter the value of the optimal solution) for a well known local graph partitioning problem.

Complexity of token swapping and its variants

In the Token Swapping problem we are given a graph with a token placed on each vertex. Each token has exactly one destination vertex, and we try to move all the tokens to their destinations, using the minimum number of swaps, i.e., operations of exchanging the tokens on two adjacent vertices. As the main result of this paper, we show that Token Swapping is

Parameterized Hardness of Art Gallery Problems

W[1]

Parameterized exact and approximation algorithms for maximum k-set cover and related satisfiability problems

-hard parameterized by the length

Complexity of Grundy Coloring and Its Variants

k

Multi-parameter Analysis for Local Graph Partitioning Problems: Using Greediness for Parameterization

of a shortest sequence of swaps. In fact, we prove that, for any computable function

Havannah and TwixT are PSPACE-complete

f

Time-approximation trade-offs for inapproximable problems

, it cannot be solved in time

Parameterized (in)approximability of subset problems

f(k)n^{o(k / \log k)}