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Adaptive local ratio
"... Local Ratio is a wellknown paradigm for designing approximation algorithms for combinatorial optimization problems. At a very high level, a local ratio algorithm first decomposes the input weight function w into a positive linear combination of simpler weight functions or models. Guided by this pro ..."
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Local Ratio is a wellknown paradigm for designing approximation algorithms for combinatorial optimization problems. At a very high level, a local ratio algorithm first decomposes the input weight function w into a positive linear combination of simpler weight functions or models. Guided by this process a solution S is constructed such that S is αapproximate with respect to each model used in the decomposition. As a result, S is αapproximate under w as well. These models usually have a very simple structure that remains “unchanged” throughout the execution of the algorithm. In this work we show that adaptively choosing a model from a richer spectrum of functions can lead to a better local ratio. Indeed, by turning the search for a good model into an optimization problem of its own, we get improved approximations for a data migration problem.
Exact and approximation algorithms for the complementary maximal strip recovery problem
, 2012
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On TreeConstrained Matchings and Generalizations
, 2011
"... We consider the following TreeConstrained Bipartite Matching problem: Given two rooted trees T1 = (V1, E1), T2 = (V2, E2) and a weight function w: V1 × V2 ↦ → R+, find a maximum weight matching M between nodes of the two trees, such that none of the matched nodes is an ancestor of another matched ..."
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We consider the following TreeConstrained Bipartite Matching problem: Given two rooted trees T1 = (V1, E1), T2 = (V2, E2) and a weight function w: V1 × V2 ↦ → R+, find a maximum weight matching M between nodes of the two trees, such that none of the matched nodes is an ancestor of another matched node in either of the trees. This generalization of the classical bipartite matching problem appears, for example, in the computational analysis of live cell video data. We show that the problem is APXhard and thus, unless P = N P, disprove a previous claim that it is solvable in polynomial time. Furthermore, we give a 2approximation algorithm based on a combination of the local ratio technique and a careful use of the structure of basic feasible solutions of a natural LPrelaxation, which we also show to have an integrality gap of 2 − o(1). In the second part of the paper, we consider a natural generalization of the problem, where trees are replaced by partially ordered sets (posets). We show that the local ratio technique gives a 2kρapproximation for the kdimensional matching generalization of the problem, in which the maximum number of incomparable elements below (or above) any given element in each poset is bounded by ρ. We finally give an almost matching integrality gap example, and an inapproximability result showing that the dependence on ρ is most likely unavoidable.
Liang J: Order independent structural alignment of circularly permuted proteins
 Conf Proc IEEE Eng Med Biol Soc 2004
"... Abstract–Circular permutation connects the N and C termini of a protein and concurrently cleaves elsewhere in the chain, providing an important mechanism for generating novel protein fold and functions. However, their in genomes is unknown because current detection methods can miss many occurances, ..."
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Abstract–Circular permutation connects the N and C termini of a protein and concurrently cleaves elsewhere in the chain, providing an important mechanism for generating novel protein fold and functions. However, their in genomes is unknown because current detection methods can miss many occurances, mistaking random repeats as circular permutation. Here we develop a method for detecting circularly permuted proteins from structural comparison. Sequence order independent alignment of protein structures can be regarded as a special case of the maximumweight independent set problem, which is known to be computationally hard. We develop an efficient approximation algorithm by repeatedly solving relaxations of an appropriate intermediate integer programming formulation, we show that the approximation ratio is much better then the theoretical worst case ratio of. Circularly permuted proteins reported in literature can be identified rapidly with our method, while they escape the detection by publicly available servers for structural alignment. Keywords–circular permuations, integer programming, linear programming, protein structure alignment
Web Monitoring 2.0: Crossing Streams to Satisfy Complex Data Needs
"... Abstract — Web Monitoring 2.0 supports the complex information needs of clients who probe information and generate mashups by integrating across multiple volatile streams. A proxy that aims at capturing multiple client profiles that are customized to each client will face a scalability challenge in ..."
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Abstract — Web Monitoring 2.0 supports the complex information needs of clients who probe information and generate mashups by integrating across multiple volatile streams. A proxy that aims at capturing multiple client profiles that are customized to each client will face a scalability challenge in trying to maximize the number of clients served while at the same time fully satisfying complex client needs. In this paper, we introduce an abstraction of complex execution intervals, a combination of time intervals and information streams, to capture complex client needs. Given some budgetary constraints (e.g., bandwidth), we present offline algorithmic solutions for the problem of maximizing completeness. I.
Improved Algorithms for Largest Cardinality 2Interval Pattern Problem
 JOURNAL OF COMBINATORIAL OPTIMIZATION
"... The 2Interval Pattern problem is to find the largest constrained pattern in a set of 2intervals. The constrained pattern is a subset of the given 2intervals such that any pair of them are Rcomparable, where model R ⊆ { <, ⊏, ()}. The problem stems from the study of general representation of ..."
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The 2Interval Pattern problem is to find the largest constrained pattern in a set of 2intervals. The constrained pattern is a subset of the given 2intervals such that any pair of them are Rcomparable, where model R ⊆ { <, ⊏, ()}. The problem stems from the study of general representation of RNA secondary structures. In this paper, we give three improved algorithms for different models. Firstly, an O(n log n + L) algorithm is proposed for the case R = { ()}, where L = O(dn) = O(n 2) is the total length of all 2intervals (density d is the maximum number of 2intervals over any point). This improves previous O(n 2 log n) algorithm. Secondly, we use dynamic programming techniques to obtain an O(n log n+dn) algorithm for the case R = { <, ⊏}, which improves previous O(n 2) result. Finally, we present another O(n log n + L) algorithm for the case R = { ⊏, () } with disjoint support(interval ground set), which improves previous O(n 2 √ n) upper bound.
Deadline Constrained Scheduling for Data Aggregation in Unreliable Sensor Networks
"... AbstractWe study the problem of maximizing the aggregated information in a wireless sensor network. We consider a sensor network with a tree topology, where the root corresponds to the sink, and the rest of the network detects an event and transmits data to the sink. We formulate an integer optimi ..."
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AbstractWe study the problem of maximizing the aggregated information in a wireless sensor network. We consider a sensor network with a tree topology, where the root corresponds to the sink, and the rest of the network detects an event and transmits data to the sink. We formulate an integer optimization problem that maximizes the aggregated information that reaches the sink under deadline and interference constraints. This framework allows using a variety of error recovery schemes to tackle link unreliability. We show that the optimal solution involves solving a Job Interval Selection Problem (JISP) which is known to be MAX SNPHard. We construct a suboptimal version, and develop a low complexity, distributed optimal solution to this version. We investigate tree structures for which this solution is optimal to the original problem. Our numerical results show that the suboptimal solution outperforms existing JISP approximation algorithms even for general trees.
Parameterized complexity in multipleinterval graphs: domination
 In Proceedings of the 6th International Symposium on Parameterized and Exact Computation
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Interval Scheduling and Colorful Independent Sets
"... Abstract. The NPhard Independent Set problem is to determine for a given graph G and an integer k whether G contains a set of k pairwise nonadjacent vertices. The problem has numerous applications in scheduling, including resource allocation and steel manufacturing. There, one encounters restricted ..."
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Abstract. The NPhard Independent Set problem is to determine for a given graph G and an integer k whether G contains a set of k pairwise nonadjacent vertices. The problem has numerous applications in scheduling, including resource allocation and steel manufacturing. There, one encounters restricted graph classes such as 2union graphs, which are edgewise unions of two interval graphs on the same vertex set, or strip graphs, where additionally one of the two interval graphs is a disjoint union of cliques. We prove NPhardness of Independent Set on a very restricted subclass of 2union graphs and identify natural parameterizations to chart the possibilities and limitations of effective polynomialtime preprocessing (kernelization) and fixedparameter algorithms. Our algorithms benefit from novel formulations of the computational problems in terms of (list)colored interval graphs. 1