Efficient Computation of Regret-ratio Minimizing Set

Asudeh, Abolfazl; Nazi, Azade; Zhang, Nan; Das, Gautam

doi:10.1145/3035918.3035932

Cited by 51 publications

(95 citation statements)

References 21 publications

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“…In this case, Algorithm 1 is the fastest over all known approximation algorithms for the k-RMS problem. For constant k, the running time is O(n + 1 γ 3(d−1)/2 log 2 1 γ ), while the best known approximation for the k-RMS problem in [3] (and [4] for the 1-RMS problem) runs in O( n γ d−1 log n log 1 ) time. In theory, k can be much larger.…”

Section: Discussionmentioning

confidence: 99%

“…A generalization of the k-RMS problem, proposed in [4,23]. The goal is to minimize the dissatisfaction of the k-th top tuple in Q versus the k-th top tuple in P, i.e.…”

Section: Top-k Rmsmentioning

confidence: 99%

“…/2 ) and they do not scale efficiently with k. A third method [3,4], models the k-RMS problem as a set cover or a hitting set problem and uses known approximation algorithms with provable guarantees. In particular, given a parameter 0 < γ < 1, in [3] the authors get a (k, (1−γ) +γ)-regret set of size O(s log s ) in O(…”

Section: Top-k Rmsmentioning

confidence: 99%

“…For a parameter γ > 0, their algorithm outputs a (k, (1−γ) +γ)-regret set in expected time O( n γ d−1 log n log 1 ). Notice that the algorithm for the 1-RMS problem presented in [4] has almost the same running time and the same approximation factor. The algorithms mentioned above spend too much time because all their operations run on the entire input set P. Our main idea is to work with two sketches P 1 , P k of the database P instead of the entire set.…”

Section: Algorithms For Rms Problemmentioning

confidence: 99%

“…Furthermore, the size of the regret sets that the HS algorithm returns is competitive, if not smaller, to the size of the regret set returned by the Greedy algorithm. Similarly, Asudeh et al [4] showed that their approximation algorithm for the 1-RMS problem, which is essentially the same as HS for k = 1, is much faster than the Greedy algorithm presented in [17]. It is clear that Hitting set type of algorithms perform much faster than greedy type algorithms, so we only compare our implementations with HS.…”

Section: Coresethsmentioning

confidence: 99%

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Faster Approximation Algorithm for the k-Regret Minimizing Set and Related Problems

Kumar

Sintos

2018

2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)

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Efficient multi-criteria decision making often requires looking at a small set of representative objects from a large collection. A recently proposed method for finding representative objects is the k-regret minimizing set (k-RMS problem). Intuitively, given a large set of objects (points) in d dimensions, the goal is to choose a small representative subset, such that for every user preference, there is always an object in the subset whose preference score is not much worse than the score of the k-th most preferred object in the original set. We propose two new efficient approximation algorithms for the k-regret minimizing set problem with provable theoretical guarantees. Our algorithms improve on the space and time complexities of previous approximation algorithms for the k-RMS problem. In addition, we run extensive experiments on real and synthetic data sets showing that simple modifications of our theoretical algorithms run significantly faster than the previous implementations of the k-RMS problem. Finally, we present an efficient approximation algorithm with theoretical guarantees for an extension of the k-RMS problem, which is called the Top-k regret minimizing set problem.

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Section: Discussionmentioning

confidence: 99%

“…A generalization of the k-RMS problem, proposed in [4,23]. The goal is to minimize the dissatisfaction of the k-th top tuple in Q versus the k-th top tuple in P, i.e.…”

Section: Top-k Rmsmentioning

confidence: 99%

Section: Top-k Rmsmentioning

confidence: 99%

Section: Algorithms For Rms Problemmentioning

confidence: 99%

Section: Coresethsmentioning

confidence: 99%

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