Paradigms for Parameterized Enumeration

Creignou, Nadia; Meier, Arne; Müller, Julian-Steffen; Schmidt, Johannes; Vollmer, Heribert

doi:10.1007/978-3-642-40313-2_27

Cited by 19 publications

(30 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We call an algorithm with a running time of the form f (k) · |x| a linear-time FPT algorithm. Creignou et al [16,Definition 3.2] introduced the concept of FPT-delay algorithms for enumeration problems. An algorithm A is an FPT-delay algorithm if there exist a computable function f and a polynomial p such that A outputs for every input x all solutions of x with at most f (k) · p(|x|) time between two successive solutions.…”

Section: Preliminariesmentioning

confidence: 99%

“…The second new notion we introduce in this paper is an adaption of an enumerative kernelization concept due to Creignou et al [16].…”

Section: Enum-advice Kernelizationmentioning

confidence: 99%

“…Creignou et al [16] developed a concept to address enumeration problems. Roughly speaking, their concept requires that all solutions of the input instance can be recovered from the input instance and the solutions of the kernel (see Figure 2(a)).…”

Section: Enum-advice Kernelizationmentioning

confidence: 99%

“…We will now give a formal definition of our new enumerative kernelization concept and then discuss the potential advantages compared to the concept by Creignou et al [16].…”

Section: Enum-advice Kernelizationmentioning

confidence: 99%

“…Consider the Enum Vertex Cover problem parameterized by solution size k; here the task is to list all minimal vertex covers of size at most k of an input graph G. As observed by Creignou et al [16,Proposition 1], the standard Buss' kernelization [18] provides an enum-kernelization for this problem. It consists of the following two data reduction rules:…”

Section: Enum-advice Kernelizationmentioning

confidence: 99%

See 4 more Smart Citations

Parameterized Aspects of Triangle Enumeration

Bentert

Fluschnik

Nichterlein

et al. 2017

Fundamentals of Computation Theory

View full text Add to dashboard Cite

Listing all triangles in an undirected graph is a fundamental graph primitive with numerous applications. It is trivially solvable in time cubic in the number of vertices. It has seen a significant body of work contributing to both theoretical aspects (e.g., lower and upper bounds on running time, adaption to new computational models) as well as practical aspects (e.g. algorithms tuned for large graphs). Motivated by the fact that the worst-case running time is cubic, we perform a systematic parameterized complexity study of triangle enumeration, providing both positive results (new enumerative kernelizations, "subcubic" parameterized solving algorithms) as well as negative results (likely uselessness in terms of "faster" parameterized algorithms of certain parameters such as graph diameter).

show abstract

Section: Preliminariesmentioning

confidence: 99%

“…The second new notion we introduce in this paper is an adaption of an enumerative kernelization concept due to Creignou et al [16].…”

Section: Enum-advice Kernelizationmentioning

confidence: 99%

Section: Enum-advice Kernelizationmentioning

confidence: 99%

“…We will now give a formal definition of our new enumerative kernelization concept and then discuss the potential advantages compared to the concept by Creignou et al [16].…”

Section: Enum-advice Kernelizationmentioning

confidence: 99%

Section: Enum-advice Kernelizationmentioning

confidence: 99%

See 3 more Smart Citations

Parameterized Aspects of Triangle Enumeration

Bentert

Fluschnik

Nichterlein

et al. 2017

Fundamentals of Computation Theory

View full text Add to dashboard Cite

show abstract

Output-sensitive complexity of multiobjective combinatorial optimization

Bökler

Ehrgott

Morris

et al. 2017

J. Multi-Crit. Decis. Anal.

View full text Add to dashboard Cite

We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is output-sensitive, that is, its running time is bounded by a polynomial in the input and the output size. We provide both practical examples of multiobjective combinatorial optimization problems for which such an efficient algorithm exists as well as problems for which no efficient algorithm exists under mild complexity theoretic assumptions. KEYWORDScombinatorial optimization, linear programming, multiobjective optimization, output-sensitive complexity 1 1.1 gives us problems, which are not harder than a variant of the problem where we also want to find solutions. Hence, proving hardness of the problem as defined in Definition 1.1 will lead to a hardness result for the problem including finding of a representative solution.

show abstract