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61
Parameterized Complexity
, 1998
"... the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs ..."
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Cited by 1213 (77 self)
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the rapidly developing systematic connections between FPT and useful heuristic algorithms  a new and exciting bridge between the theory of computing and computing in practice. The organizers of the seminar strongly believe that knowledge of parameterized complexity techniques and results belongs into the toolkit of every algorithm designer. The purpose of the seminar was to bring together leading experts from all over the world, and from the diverse areas of computer science that have been attracted to this new framework. The seminar was intended as the rst larger international meeting with a specic focus on parameterized complexity, and it hopefully serves as a driving force in the development of the eld. 1 We had 49 participants from Australia, Canada, India, Israel, New Zealand, USA, and various European countries. During the workshop 25 lectures were given. Moreover, one night session was devoted to open problems and Thursday was basically used for problem discussion
On the parameterized complexity of multipleinterval graph problems
 Theor. Comput. Sci
"... Abstract. Multipleinterval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it. Many applications of interval graphs also generalize to multipleinterval graphs, often allowing for more robustness in the modeling of the specifi ..."
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Cited by 50 (8 self)
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Abstract. Multipleinterval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it. Many applications of interval graphs also generalize to multipleinterval graphs, often allowing for more robustness in the modeling of the specific application. With this motivation in mind, a recent systematic study of optimization problems in multipleinterval graphs was initiated. In this sequel, we study multipleinterval graph problems from the perspective of parameterized complexity. The problems under consideration are kIndependent Set, kDominating Set, and kClique, which are all known to be W[1]hard for general graphs, and NPcomplete for multipleinterval graphs. We prove that kClique is in FPT, while kIndependent Set and kDominating Set are both W[1]hard. We also prove that kIndependent Dominating Set, a hybrid of the two above problems, is also W[1]hard. Our hardness results hold even when each vertex is associated with at most two intervals, and all intervals have unit length. Furthermore, as an interesting byproduct of our hardness results, we develop a useful technique for showing W[1]hardness via a reduction from the kMulticolored Clique problem, a variant of kClique. We believe this technique has interest in its own right, as it should help in simplifying W[1]hardness results which are notoriously hard to construct and technically tedious.
An efficient approximation for the generalized assignment problem
 Information Processing Letters
, 2006
"... We present a simple family of algorithms for solving the Generalized Assignment Problem (GAP). Our technique is based on a novel combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for GAP. If the approximation ratio of the knapsack algorithm is α and ..."
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Cited by 33 (6 self)
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We present a simple family of algorithms for solving the Generalized Assignment Problem (GAP). Our technique is based on a novel combinatorial translation of any algorithm for the knapsack problem into an approximation algorithm for GAP. If the approximation ratio of the knapsack algorithm is α and its running time is O(f(N)), our algorithm guarantees a (1 + α) approximation ratio, and it runs in O(M · f(N) + M · N), where N is the number of items and M is the number of bins. Not only does our technique comprise a general interesting framework for the GAP problem; it also matches the best combinatorial approximation for this problem, with a much simpler algorithm and a better running time.
On the equivalence between the primaldual schema and the local ratio technique
 In 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX). Number 2129 in Lecture Notes in Computer Science
, 2001
"... Abstract. We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primaldual schema and the local ratio technique. Recently, primaldual algorithms were devised by first constructing a local ratio algorithm and then transform ..."
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Cited by 31 (8 self)
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Abstract. We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primaldual schema and the local ratio technique. Recently, primaldual algorithms were devised by first constructing a local ratio algorithm and then transforming it into a primaldual algorithm. This was done in the case of the 2approximation algorithms for the feedback vertex set problem and in the case of the first primaldual algorithms for maximization problems. Subsequently, the nature of the connection between the two paradigms was posed as an open question by Williamson [Math. Program., 91 (2002), pp. 447–478]. In this paper we answer this question by showing that the two paradigms are equivalent.
Optimization problems in multipleinterval graphs
 In Proceedings of the 18th annual Symposium On Discrete Algorithms (SODA
, 2007
"... Multipleinterval graphs are a natural generalization of interval graphs where each vertex may have more then one interval associated with it. We initiate the study of optimization problems in multipleinterval graphs by considering three classical problems: Minimum Vertex Cover, Minimum Dominating ..."
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Cited by 18 (5 self)
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Multipleinterval graphs are a natural generalization of interval graphs where each vertex may have more then one interval associated with it. We initiate the study of optimization problems in multipleinterval graphs by considering three classical problems: Minimum Vertex Cover, Minimum Dominating Set, and Maximum Clique. We describe applications for each one of these problems, and then proceed to discuss approximation algorithms for them. Our results can be summarized as follows: Let t be the number of intervals associated with each vertex in a given multipleinterval graph. For Minimum Vertex Cover, we give a (2 − 1/t)approximation algorithm which also works when a tinterval representation of our given graph is absent. Following this, we give a t 2approximation algorithm for Minimum Dominating Set which adapts well to more general variants of the problem. We then proceed to prove that Maximum Clique is NPhard already for 3interval graphs, and provide a (t 2 −t+ 1)/2approximation algorithm for general values of t ≥ 2, using bounds proven for the socalled transversal number of tinterval families.
On Linear and Semidefinite Programming Relaxations for Hypergraph Matching
"... The hypergraph matching problem is to find a largest collection of disjoint hyperedges in a hypergraph. This is a wellstudied problem in combinatorial optimization and graph theory with various applications. The best known approximation algorithms for this problem are all local search algorithms. I ..."
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Cited by 16 (0 self)
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The hypergraph matching problem is to find a largest collection of disjoint hyperedges in a hypergraph. This is a wellstudied problem in combinatorial optimization and graph theory with various applications. The best known approximation algorithms for this problem are all local search algorithms. In this paper we analyze different linear and semidefinite programming relaxations for the hypergraph matching problem, and study their connections to the local search method. Our main results are the following: • We consider the standard linear programming relaxation of the problem. We provide an algorithmic proof of a result of Füredi, Kahn and Seymour, showing that the integrality gap is exactly k − 1 + 1/k for kuniform hypergraphs, and is exactly k − 1 for kpartite hypergraphs. This yields an improved approximation algorithm for the weighted 3dimensional matching problem. Our algorithm combines the use of the iterative rounding method and the fractional local ratio method, showing a new way to round linear programming solutions for packing problems. • We study the strengthening of the standard LP relaxation by local constraints. We show that, even after linear number of rounds of the SheraliAdams liftandproject procedure on the standard LP relaxation, there are kuniform hypergraphs with integrality gap at least k − 2. On the other hand, we prove that for every constant k, there is a strengthening of the standard LP relaxation by only a polynomial number of constraints, with integrality gap at most (k+1)/2 for kuniform hypergraphs. The construction uses a result in extremal combinatorics. • We consider the standard semidefinite programming relaxation of the problem. We prove that the Lovász ϑfunction provides an SDP relaxation with integrality gap at most (k + 1)/2. The proof gives an indirect way (not by a rounding algorithm) to bound the ratio between any local optimal solution and any optimal SDP solution. This shows a new connection between local search and linear and semidefinite programming relaxations. 1
Efficient and Strategyproof Spectrum Allocations in Multichannel Wireless Networks
"... Abstract—In this paper, we study the spectrum assignment problem for wireless access networks. We assume that each secondary user will bid a certain value for exclusive usage of some spectrum channels for a certain time period or for a certain time duration. A secondary user may also require the exc ..."
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Cited by 15 (4 self)
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Abstract—In this paper, we study the spectrum assignment problem for wireless access networks. We assume that each secondary user will bid a certain value for exclusive usage of some spectrum channels for a certain time period or for a certain time duration. A secondary user may also require the exclusive usage of a subset of channels, or require the exclusive usage of a certain number of channels. Thus, several versions of problems are formulated under various different assumptions. For the majority of problems, we design PTAS or efficient constantapproximation algorithms such that overall profit is maximized. Here, the profit is defined as the total bids of all satisfied secondary users. As a side product of our algorithms, we are able to show that a previously studied Scheduling Split Interval Problem (SSIP) [2], in which each job is composed of t intervals, cannot be approximated within Oðt1 Þ for any small>0 unless NP ZPP. Opportunistic spectrum usage, although a promising technology, could suffer from the selfish behavior of secondary users. In order to improve opportunistic spectrum usage, we then propose to combine the game theory with wireless modeling. We show how to design a truthful mechanism based on all of these algorithms such that the best strategy of each secondary user to maximize its own profit is to truthfully report its actual bid.
Approximating the 2interval pattern problem
 IN PROCEEDINGS OF THE 13TH ANNUAL EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA
, 2005
"... We address the problem of approximating the 2Interval Pattern problem over its various models and restrictions. This problem, which is motivated by RNA secondary structure prediction, asks to find a maximum cardinality subset of a 2interval set with respect to some prespecified model. For each s ..."
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Cited by 15 (6 self)
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We address the problem of approximating the 2Interval Pattern problem over its various models and restrictions. This problem, which is motivated by RNA secondary structure prediction, asks to find a maximum cardinality subset of a 2interval set with respect to some prespecified model. For each such model, we give varying approximation quality depending on the different possible restrictions imposed on the input 2interval set.
Looking at the stars
"... The problem of packing vertexdisjoint copies of a graph into another graph is NPcomplete if has more than two vertices in some connected component. In the framework of parameterized complexity we analyze a particular family of instances of this problem, namely the packing of stars. We give a ..."
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Cited by 14 (0 self)
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The problem of packing vertexdisjoint copies of a graph into another graph is NPcomplete if has more than two vertices in some connected component. In the framework of parameterized complexity we analyze a particular family of instances of this problem, namely the packing of stars. We give a quadratic kernel for packing copies of When we consider the special case of , i.e. being a star with two leaves, we give a linear kernel and an algorithm running in time ff flfi
Topology independent protein structural alignment
 BMC Bioinformatics
, 2007
"... Abstract. Protein structural alignment is an indispensable tool used for many different studies in bioinformatics. Most structural alignment algorithms assume that the structural units of two similar proteins will align sequentially. This assumption may not be true for all similar proteins and as a ..."
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Cited by 13 (2 self)
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Abstract. Protein structural alignment is an indispensable tool used for many different studies in bioinformatics. Most structural alignment algorithms assume that the structural units of two similar proteins will align sequentially. This assumption may not be true for all similar proteins and as a result, proteins with similar structure but with permuted sequence arrangement are often missed. We present a solution to the problem based on an approximation algorithm that finds a sequenceorder independent structural alignment that is close to optimal. We first exhaustively fragment two proteins and calculate a novel similarity score between all possible aligned fragment pairs. We treat each aligned fragment pair as a vertex on a graph. Vertices are connected by an edge if there are intra residue sequence conflicts. We regard the realignment of the fragment pairs as a special case of the maximumweight independent set problem and solve this computationally intensive problem approximately by iteratively solving relaxations of an appropriate integer programming formulation. The resulting structural alignment is sequence order independent. Our method is insensitive to gaps, insertions/deletions, and circular permutations. 1