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177
Improved algorithms and analysis for the laminar matroid secretary problem
, 2013
"... In a matroid secretary problem, one is presented with a sequence of objects of various weights in a random order, and must choose irrevocably to accept or reject each item. There is a further constraint that the set of items selected must form an independent set of an associated matroid. Constant ..."
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competitive algorithms (algorithms whose expected solution weight is within a constant factor of the optimal) are known for many types of matroid secretary problems. We examine the laminar matroid and show an algorithm achieving provably 0.053 competitive ratio. 1
Secretary Problems: Laminar Matroid and Interval Scheduling
"... The classical secretary problem studies the problem of hiring the best secretary from among the secretaries who arrive in random order by making immediate and irrevocable decisions. After the interesting connection to online mechanism design was found [19, 20], the random order input assumption has ..."
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Cited by 14 (0 self)
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, as is the case in the knapsack secretary problem [3, 6]. In this paper, we consider two interesting secretary problems. One is when the matroid is a laminar matroid, which generalizes uniform / partition / truncated partition matroids. For the laminar matroid secretary problem, using a novel replacement rule
Advances on Matroid Secretary Problems: Free Order Model and Laminar Case
, 2012
"... The most wellknown conjecture in the context of matroid secretary problems claims the existence of a constantfactor approximation applicable to any matroid. Whereas this conjecture remains open, modified forms of it were shown to be true, when assuming that the assignment of weights to the secreta ..."
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Cited by 6 (1 self)
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are interviewed. Furthermore, we consider the classical matroid secretary problem for the special case of laminar matroids. Only recently, a constantfactor approximation has been found for this case, using a clever but rather involved method and analysis [12] that leads to a 16000/3approximation
The simulated greedy algorithm for several submodular matroid secretary problems. arXiv preprint arXiv:1107.2188
, 2011
"... We study the matroid secretary problems with submodular valuation functions. In these problems, the elements arrive in random order. When one element arrives, we have to make an immediate and irrevocable decision on whether to accept it or not. The set of accepted elements must form an independent ..."
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Cited by 4 (0 self)
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problems. In particular, we obtain constant competitive algorithms for the cases of laminar matroids and transversal matroids. Our algorithms can be further applied to any independent set system defined by the intersection of a constant number of laminar matroids, while still achieving constant
Matroid Secretary for Regular and Decomposable Matroids
"... In the matroid secretary problem we are given a stream of elements and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from the assumption that decisions are irrevocable: if we choose ..."
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Cited by 5 (0 self)
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In the matroid secretary problem we are given a stream of elements and asked to choose a set of elements that maximizes the total value of the set, subject to being an independent set of a matroid given in advance. The difficulty comes from the assumption that decisions are irrevocable: if we
Matchings, Matroids and Unimodular Matrices
, 1995
"... We focus on combinatorial problems arising from symmetric and skewsymmetric matrices. For much of the thesis we consider properties concerning the principal submatrices. In particular, we are interested in the property that every nonsingular principal submatrix is unimodular; matrices having this p ..."
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Cited by 13 (1 self)
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this property are called principally unimodular. Principal unimodularity is a generalization of total unimodularity, and we generalize key polyhedral and matroidal results on total unimodularity. Highlights include a generalization of Hoffman and Kruskal's result on integral polyhedra, a generalization
The Matroid Median Problem
"... In the classical kmedian problem, we are given a metric space and would like to openk centers so as to minimize the sum (over all the vertices) of the distance of each vertex to its nearest open center. In this paper, we consider the following generalization of the problem: instead of opening at mo ..."
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Cited by 10 (2 self)
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constantfactor approximation algorithm. Even more generally, what if the set of open centers had to form an independent set from a matroid? In this paper, we give a constant factor approximation algorithm for such matroid median problems. Our algorithm is based on rounding a natural LP relaxation in two
On Variants of the Matroid Secretary Problem
"... Abstract. We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constantfactorcompetitivealgorithmforthe“randomassignment”model where the weights are assigned randomly to the elements of a matroid, and then the elements arrive ..."
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Cited by 2 (0 self)
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Abstract. We present a number of positive and negative results for variants of the matroid secretary problem. Most notably, we design a constantfactorcompetitivealgorithmforthe“randomassignment”model where the weights are assigned randomly to the elements of a matroid, and then the elements arrive
Matchings, Matroids and Submodular Functions
, 2008
"... This thesis focuses on three fundamental problems in combinatorial optimization: nonbipartite matching, matroid intersection, and submodular function minimization. We develop simple, efficient, randomized algorithms for the first two problems, and prove new lower bounds for the last two problems. F ..."
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Cited by 1 (0 self)
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This thesis focuses on three fundamental problems in combinatorial optimization: nonbipartite matching, matroid intersection, and submodular function minimization. We develop simple, efficient, randomized algorithms for the first two problems, and prove new lower bounds for the last two problems
Results 1  10
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177