An Exact Method for the Minimum Feedback Arc Set Problem

Baharev, Ali; Schichl, Hermann; Neumaier, Arnold; Achterberg, Tobias

doi:10.1145/3446429

Cited by 15 publications

(15 citation statements)

References 75 publications

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“…e minimal feedback arc set problem is to nd, given a directed graph G = (V , E), a minimal subset of edges E ⊆ E such that G = (V , E \ E ) is acyclic. at is, adding any edge e ∈ E back to G creates a cycle [Baharev et al, 2015]. Our maximal children problem has the additional constraint that only edges in the tier T can be removed from the edges of the graph.…”

mentioning

confidence: 99%

Practical Algorithms for Multi-Stage Voting Rules with Parallel Universes Tiebreaking

Wang

Sikdar

Shepherd

et al. 2019

AAAI

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STV and ranked pairs (RP) are two well-studied voting rules for group decision-making. They proceed in multiple rounds, and are affected by how ties are broken in each round. However, the literature is surprisingly vague about how ties should be broken. We propose the first algorithms for computing the set of alternatives that are winners under some tiebreaking mechanism under STV and RP, which is also known as parallel-universes tiebreaking (PUT). Unfortunately, PUTwinners are NP-complete to compute under STV and RP, and standard search algorithms from AI do not apply. We propose multiple DFS-based algorithms along with pruning strategies, heuristics, sampling and machine learning to prioritize search direction to significantly improve the performance. We also propose novel ILP formulations for PUT-winners under STV and RP, respectively. Experiments on synthetic and realworld data show that our algorithms are overall faster than ILP.

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confidence: 99%

Practical Algorithms for Multi-Stage Voting Rules with Parallel Universes Tiebreaking

Wang

Sikdar

Shepherd

et al. 2019

AAAI

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“…Thus, the conditions O(G) = ∅ and O el (G) = ∅ are equivalent. The FVSP & FASP can be also formulated in terms of the maximum linear ordering problem see for instance [4,43].…”

Section: Problem Formulationmentioning

confidence: 99%

“…Further, [14] proposes the most common state of the art heuristic termed Greedy Removal (GR). Exact methods use ILP-solvers with modern formulations given in [4,40] based on the results of [19,43]. However, for dense or large sparse graphs the ILP-approaches run into time out while the heuristical approach GR performs inaccurately.…”

Section: Introductionmentioning

confidence: 99%

Tight Localizations of Feedback Sets

Hecht¹,

Gonciarz²,

Horvát³

2020

Preprint

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The classical NP-hard feedback arc set problem (FASP) and feedback vertex set problem (FVSP) ask for a minimum set of arcs ε ⊆ E or vertices ν ⊆ V whose removal G \ ε, G \ ν makes a given multi-digraph G = (V , E) acyclic, respectively. The corresponding decision problems are part of the 21 NP-complete problems of R. M. Karp's famous list. Though both problems are known to be APX-hard, approximation algorithms or proofs of inapproximability are unknown. We propose a new O(|V ||E| 4 )-heuristic for the directed FASP. While r ≈ 1.3606 is known to be a lower bound for the APX-hardness, at least by validation, we show that r ≤ 2. Applying the approximation preserving L-reduction from the directed FVSP to the FASP thereby allows computing feedback vertex sets with the same accuracy.Benchmarking the algorithm with state of the art alternatives yields that, for the first time, the most relevant instance class of large sparse graphs can be solved efficiently within tight error bounds. Our derived insights might provide a path to prove the APX-completeness of both problems.

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“…Remark 4.1: Feedback arc set along with feedback vertex set are two important concepts in graph theory, which have been widely studied. In [51], an exact method for the minimum feedback arc set has been proposed for large and sparse digraphs, based on linear programming method. In [51], Baharev et al tested several different sizes of digraph to find a minimal feedback arc set.…”

Section: Amentioning

confidence: 99%

“…In [51], an exact method for the minimum feedback arc set has been proposed for large and sparse digraphs, based on linear programming method. In [51], Baharev et al tested several different sizes of digraph to find a minimal feedback arc set. For example the cardinality of the minimal feedback arc set is 12 in a digraph with 109 nodes.…”

Section: Amentioning

confidence: 99%

A New Approach to Pinning Control of Boolean Networks

Zhong

2019

Preprint

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Boolean networks (BNs) are discrete-time systems where gene nodes are inter-connected (here we call such connection rule among nodes as network structure), and the dynamics of each gene node is determined by logical functions. In this paper, we propose a new framework on pinning control design for global stabilization of BNs based on BNs' network structure (named as NS-based distributed pinning control). By deleting the minimum number of edges, the network structure becomes acyclic. Then, a NS-based distributed pinning control is designed to achieve global stabilization. Compared with existing literature, the design of NS-based distributed pinning control is not based on the state transition matrix of BNs. Hence, the computational complexity in this paper is reduced fromwhere n is the number of nodes and K < n is the largest number of in-neighbors of nodes in a BN. In addition, without using state transition matrix, global state information is no longer needed, and the design of pinning control is just based on neighbors' local information, which is easier to be implemented. The proposed method is well demonstrated by several biological networks with different network sizes. The results are shown to be simple and concise, while the traditional pinning control can not be implemented for BNs with such a large dimension.

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An Exact Method for the Minimum Feedback Arc Set Problem

Cited by 15 publications

References 75 publications

Practical Algorithms for Multi-Stage Voting Rules with Parallel Universes Tiebreaking

Practical Algorithms for Multi-Stage Voting Rules with Parallel Universes Tiebreaking

Tight Localizations of Feedback Sets

A New Approach to Pinning Control of Boolean Networks

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