On an Optimal Split Tree Problem

Kosaraju, S. Rao; Przytycka, Teresa M.; Borgstrom, Ryan S.

doi:10.1007/3-540-48447-7_17

Cited by 51 publications

(60 citation statements)

References 11 publications

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“…To get a better understanding of the performance results, we generate multiple permuatations of scenario distributions for the same value of α. For the ODT problem, we also use a synthetic dataset -SYN-K -that is parameterized by k; this is based on a hard instance for the greedy algorithm [23]. Given k, we generate m = 2k + 3 sets, n = k + 2 elements, with 4k + 4 non-zeros as follows: (a) elements i ∈ [1, k] are contained in scenarios 2i − 1 and 2i, (b) element k + 1 is contained in all odd numbered scenarios, and (c) element k + 2 is contained in all even numbered scenarios and scenario 2k + 3.…”

Section: Methodsmentioning

confidence: 99%

“…In this paper, we study an adaptive optimization problem in the setting described above which simultaneously generalizes many previously-studied problems such as optimal decision trees [20,23,10,8,18,9], equivalence class determination [14,7], decision region determination [22] and submodular ranking [3,21]. We obtain an algorithm with the best-possible approximation guarantee.…”

Section: Introductionmentioning

confidence: 99%

“…Such a simple algorithm was previously unknown even in the special case of optimal decision tree (under arbitrary costs/probabilities), despite a large number of papers [20,23,10,1,8,16,18,13,9] on this topic. The first O(log m)-approximation algorithm for ODT was obtained in [18], and this result was extended to the equivalence class determination problem in [9].…”

Section: Introductionmentioning

confidence: 99%

“…Previous results, eg. [23,10,1,8,16], based on a simple greedy "splitting" algorithm, had a logarithmic dependence on either costs or probabilities which (in the worst case) can be exponential in m.…”

Section: Introductionmentioning

confidence: 99%

“…The other line of work is on the optimal decision tree problem and its variants, eg. [23,10,18,13,9]. In particular, we combine the time-based analysis for the deterministic submodular ranking problem in [21] with the phase-based analysis for optimal decision tree in [23,18,9].…”

Section: Introductionmentioning

confidence: 99%

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Adaptive Submodular Ranking

Kambadur

Nagarajan

Navidi

2017

Integer Programming and Combinatorial Optimization

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We study a general adaptive ranking problem where an algorithm needs to perform a sequence of actions on a random user, drawn from a known distribution, so as to "satisfy" the user as early as possible. The satisfaction of each user is captured by an individual submodular function, where the user is said to be satisfied when the function value goes above some threshold. We obtain a logarithmic factor approximation algorithm for this adaptive ranking problem, which is the best possible. The adaptive ranking problem has many applications in active learning and ranking: it significantly generalizes previously-studied problems such as optimal decision trees, equivalence class determination, decision region determination and submodular cover. We also present some preliminary experimental results based on our algorithm.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive Submodular Ranking

Kambadur

Nagarajan

Navidi

2017

Integer Programming and Combinatorial Optimization

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Scenario Submodular Cover

Grammel¹,

Hellerstein²,

Kletenik

et al. 2017

Approximation and Online Algorithms

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Many problems in Machine Learning can be modeled as submodular optimization problems. Recent work has focused on stochastic or adaptive versions of these problems. We consider the Scenario Submodular Cover problem, which is a counterpart to the Stochastic Submodular Cover problem studied by Golovin and Krause (2011). In Scenario Submodular Cover, the goal is to produce a cover with minimum expected cost, where the expectation is with respect to an empirical joint distribution, given as input by a weighted sample of realizations. In contrast, in Stochastic Submodular Cover, the variables of the input distribution are assumed to be independent, and the distribution of each variable is given as input. Building on algorithms developed by Cicalese et al. (2014) and Golovin and Krause (2011) for related problems, we give two approximation algorithms for Scenario Submodular Cover over discrete distributions. The first achieves an approximation factor of O(log Qm), where m is the size of the sample and Q is the goal utility. The second, simpler algorithm achieves an approximation bound of O(log QW ), where Q is the goal utility and W is the sum of the integer weights. (Both bounds assume an integer-valued utility function.) Our results yield approximation bounds for other problems involving non-independent distributions that are explicitly specified by their support.

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An Approximation Algorithm for Binary Searching in Trees

Laber

Molinaro

2008

Automata, Languages and Programming

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On an Optimal Split Tree Problem

Cited by 51 publications

References 11 publications

Adaptive Submodular Ranking

Adaptive Submodular Ranking

Scenario Submodular Cover

An Approximation Algorithm for Binary Searching in Trees

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