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On parameterized approximability
 Proc. of IWPEC, Lecture Notes in Computer Science 4169
, 2006
"... Abstract. Combining classical approximability questions with parameterized complexity, we introduce a theory of parameterized approximability. The main intention of this theory is to deal with the efficient approximation of small cost solutions for optimisation problems. Key words. Fixedparameter t ..."
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Cited by 21 (5 self)
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Abstract. Combining classical approximability questions with parameterized complexity, we introduce a theory of parameterized approximability. The main intention of this theory is to deal with the efficient approximation of small cost solutions for optimisation problems. Key words. Fixed
Parameterized approximation problems
 In Parameterized and Exact Computation, Second International Workshop, IWPEC 2006
, 2006
"... Parameterized complexity is fast becoming accepted as an important strand in the mainstream of algorithm design and analysis, alongside approximation, randomization, and the like. It is fair to say that most of the work in the area has focussed on exact algorithms for decision problems. On the other ..."
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Cited by 22 (1 self)
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Parameterized complexity is fast becoming accepted as an important strand in the mainstream of algorithm design and analysis, alongside approximation, randomization, and the like. It is fair to say that most of the work in the area has focussed on exact algorithms for decision problems
Parameterized approximation of dominating set problems
 INFORM. PROCESS. LETT
, 2008
"... A problem open for many years is whether there is an FPT algorithm that given a graph G and parameter k, either: (1) determines that G has no kDominating Set, or (2) produces a dominating set of size at most g(k), where g(k) is some fixed function of k. Such an outcome is termed an FPT approximat ..."
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Cited by 15 (2 self)
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approximation algorithm. We describe some results that begin to provide some answers. We show that there is no such FPT algorithm for g(k) of the form k + c (where c is a fixed constant, termed an additive FPT approximation), unless FPT = W[2]. We answer the analogous problem completely for the related
Parameterized approximability of the disjoint cycle problem
 Proc. ICALP 2007, Lecture Notes in Computer Science
, 2007
"... Abstract. We give an fpt approximation algorithm for the directed vertex disjoint cycle problem. Given a directed graph G with n vertices and a positive integer k, the algorithm constructs a family of at least k/ρ(k) disjoint cycles of G if the graph G has a family of at least k disjoint cycles (and ..."
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], and to the best of our knowledge our algorithm is the first fpt approximation algorithm for a natural W[1]hard problem. Key words: approximation algorithms, fixedparameter tractability, parameterized complexity theory. 1
Parameterized approximability of influence in social networks
 In Proc. 19th COCOON, volume 7936 of LNCS
, 2013
"... Abstract. In this paper, we consider the problem of maximizing the spread of influence through a social network. This optimization problem is formally defined as follows. We are given a graph G = (V,E), a positive integer k and a threshold value thr(v) attached to each vertex v ∈ V. The objective is ..."
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Cited by 1 (1 self)
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even for very restrictive thresholds. For unanimity thresholds, we prove that the problem is inapproximable in polynomial time and the decision version is W[1]hard w.r.t. parameter k. On the positive side, it becomes r(n)approximable in fpttime w.r.t. parameter k for any strictly increasing function
Parameterized Approximation Schemes using Graph Widths
"... Abstract. Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability of a number of problems which are known to be hard ..."
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Abstract. Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability of a number of problems which are known to be hard
Parameterized Approximation via Fidelity Preserving Transformations
 PROC. OF ICALP (1) 2012
, 2012
"... We motivate and describe a new parameterized approximation paradigm which studies the interaction between performance ratio and running time for any parameterization of a given optimization problem. As a key tool, we introduce the concept of αshrinking transformation, for α ≥ 1. Applying such tra ..."
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Cited by 3 (0 self)
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We motivate and describe a new parameterized approximation paradigm which studies the interaction between performance ratio and running time for any parameterization of a given optimization problem. As a key tool, we introduce the concept of αshrinking transformation, for α ≥ 1. Applying
Parameterized approximation scheme for the multiple knapsack problem
 IN PROCEEDINGS OF THE 20TH ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS, SODA 2009
, 2009
"... The multiple knapsack problem (MKP) is a wellknown generalization of the classical knapsack problem. We are given a set A of n items and set B of m bins (knapsacks) such that each item a ∈ A has a size size(a) and a profit value profit(a), and each bin b ∈ B has a capacity c(b). The goal is to find ..."
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Cited by 9 (2 self)
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The multiple knapsack problem (MKP) is a wellknown generalization of the classical knapsack problem. We are given a set A of n items and set B of m bins (knapsacks) such that each item a ∈ A has a size size(a) and a profit value profit(a), and each bin b ∈ B has a capacity c(b). The goal is to find a subset U ⊂ A of maximum total profit such that U can be packed into B without exceeding the capacities. The decision version of MKP is strongly NPcomplete, since it is a generalization of the classical knapsack and bin packing problem. Furthermore, MKP does not admit an FPTAS even if the number m of bins is two. Kellerer gave a PTAS for MKP with identical capacities and Chekuri and Khanna presented a PTAS for MKP with general capacities with running time n O(log(1/ǫ)/ǫ8). In this
Parameterized Approximability of Maximizing the Spread of Influence in Networks
"... Abstract. In this paper, we consider the problem of maximizing the spread of influence through a social network. Here, we are given a graph G = (V, E), a positive integer k and a threshold value thr(v) attached to each vertex v ∈ V. The objective is then to find a subset of k vertices to “activate ” ..."
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Cited by 6 (2 self)
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thresholds, we prove that the problem is inapproximable in polynomial time and the decision version is W[1]hard w.r.t. parameter k. On the positive side, it becomes r(n)approximable in fpttime w.r.t. parameter k for any strictly increasing function r. Moreover, we give an fpttime algorithm to solve
Beyond Fuzzy: Parameterized Approximations of Heyting Algebras for Uncertain Knowledge
"... Abstract. We propose a parameterized framework based on a Heyting algebra and Lukasiewicz negation for modeling uncertainty for belief. We adopt a probability theory as mathematical formalism for manipulating uncertainty. An agent can express the uncertainty in her knowledge about a piece of informa ..."
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on residuumimplication. The underlying algebra for belief computation is a parameterized approximation of strict (without negation) Heyting (or briefly ’parameterized Heyting’) algebra with a unique epistemic negation: it is a set of Lukasiewiczstyle residuated lattices and extension of fuzzy logic
Results 1  10
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1,952