21.04.2023

Five Papers accepted at PODC, SEA, FORC and WADS

We are happy to announce five recently accepted papers: First, one paper will appear at the ACM Symposium on Principles of Distributed Computing on 19-23 June in Orlando, USA. The paper with the title The Impact of Cooperation in Bilateral Network Creation is based on the master thesis of Arthur Zahn and investigates the formation of bilateral networks among selfish agents (e.g. social networks) from a game-theoretic point of view. It focuses mainly on the trade-off between the amount of cooperation and the Price of Anarchy by analyzing different solution concepts that capture various degrees of cooperation among the agents.

A second paper titled Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex Cover was accepted at the 21st Symposium on Experimental Algorithms (SEA) which will take place on 24-26 July in Barcelona, Spain. The paper was written by our students about the algorithm with which they also won the third place in the exact track of the PACE Challenge 2022. The algorithm is for the directed feedback vertex set problem using the idea of iterative reduction to vertex cover. They perform computational experiments showing that they outperform other approaches for those directed graphs having a low density of uni-directed edges.

Furthermore, the paper Fair Correlation Clustering in Forests was accepted at the Symposium on Foundations of Responsible Computing (FORC) on 7-9 June in Stanford, USA. The paper which is based on the master thesis of Simon Wietheger, studies the established Correlation Clustering problem under fairness constraints, i.e. requiring that in a vertex colored graph the color distribution in each computed cluster should match the color distribution of the complete vertex set. The authors demonstrate the NP-hardness of the problem even on restricted classes of forests and when relaxing the fairness constraint to only roughly match the color ratio as well as they provide polynomial time algortihms for forests under certain assumptions on the color distribution.

Finally at the Algorithms and Data Structures Symposium (WADS) which will take place on 31 July - 2 August in Montreal, Canada, two papers were accepted. In the first, Compact Distance Oracles with Large Sensitivity and Low Stretch, the authors present an \(f\)-edge fault-tolerant distance sensitivity oracle with large sensitivity, low stretch, and non-trivial query time. Such an oracle is a way of preprocessing a graph to efficiently answer distance queries approximately even when up to \(f\) edges are removed for the query.

In the second paper titled Socially Fair Matching: Exact and Approximation Algorithms, the authors introduce a variant of the Maximum Matching problem that models the social fairness objective: The goal is to find a perfect matching as well as an assignment that assigns the cost of each matched edge to one of its endpoints, such that the maximum of the total cost assigned to either of the two groups is minimized. They show that despite being weakly NP-hard, the problem admits a deterministic PTAS and a randomized FPTAS.

Clean Citation Style 005

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Friedrich, Tobias; Gawendowicz, Hans; Lenzner, Pascal; Zahn, Arthur The Impact of Cooperation in Bilateral Network CreationACM Symposium on Principles of Distributed Computing (PODC) 2023

[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]

Many real-world networks, like the Internet or social networks, are not the result of central design but instead the outcome of the interaction of local agents that selfishly optimize their individual utility. The well-known Network Creation Game by Fabrikant, Luthra, Maneva, Papadimitriou, and Shenker [PODC 2003] models this. There, agents corresponding to network nodes buy incident edges towards other agents for a price of \(\alpha > 0\) and simultaneously try to minimize their buying cost and their total hop distance. Since in many real-world networks, e.g., social networks, consent from both sides is required to establish and maintain a connection, Corbo and Parkes [PODC 2005] proposed a bilateral version of the Network Creation Game, in which mutual consent and payment are required in order to create edges. It is known that this cooperative version has a significantly higher Price of Anarchy compared to the unilateral version. On the first glance this is counter-intuitive, since cooperation should help to avoid socially bad states. However, in the bilateral version only a very restrictive form of cooperation is considered. We investigate this trade-off between the amount of cooperation and the Price of Anarchy by analyzing the bilateral version with respect to various degrees of cooperation among the agents. With this, we provide insights into what kind of cooperation is needed to ensure that socially good networks are created. As a first step in this direction, we focus on tree networks and present a collection of asymptotically tight bounds on the Price of Anarchy that precisely map the impact of cooperation. Most strikingly, we find that weak forms of cooperation already yield a significantly improved Price of Anarchy. In particular, the cooperation of coalitions of size 3 is enough to achieve constant bounds. Moreover, for general networks we show that enhanced cooperation yields close to optimal networks for a wide range of edge prices. Along the way, we disprove an old conjecture by Corbo and Parkes [PODC 2005].

@inproceedings{friedrich2023impact,
  abstract = {Many real-world networks, like the Internet or social networks, are not the result of central design but instead the outcome of the interaction of local agents that selfishly optimize their individual utility. The well-known Network Creation Game by Fabrikant, Luthra, Maneva, Papadimitriou, and Shenker [PODC 2003] models this. There, agents corresponding to network nodes buy incident edges towards other agents for a price of \(\alpha > 0\) and simultaneously try to minimize their buying cost and their total hop distance. Since in many real-world networks, e.g., social networks, consent from both sides is required to establish and maintain a connection, Corbo and Parkes [PODC 2005] proposed a bilateral version of the Network Creation Game, in which mutual consent and payment are required in order to create edges. It is known that this cooperative version has a significantly higher Price of Anarchy compared to the unilateral version. On the first glance this is counter-intuitive, since cooperation should help to avoid socially bad states. However, in the bilateral version only a very restrictive form of cooperation is considered. We investigate this trade-off between the amount of cooperation and the Price of Anarchy by analyzing the bilateral version with respect to various degrees of cooperation among the agents. With this, we provide insights into what kind of cooperation is needed to ensure that socially good networks are created. As a first step in this direction, we focus on tree networks and present a collection of asymptotically tight bounds on the Price of Anarchy that precisely map the impact of cooperation. Most strikingly, we find that weak forms of cooperation already yield a significantly improved Price of Anarchy. In particular, the cooperation of coalitions of size 3 is enough to achieve constant bounds. Moreover, for general networks we show that enhanced cooperation yields close to optimal networks for a wide range of edge prices. Along the way, we disprove an old conjecture by Corbo and Parkes [PODC 2005].},
  author = {Friedrich, Tobias and Gawendowicz, Hans and Lenzner, Pascal and Zahn, Arthur},
  booktitle = {ACM Symposium on Principles of Distributed Computing (PODC)},
  keywords = {hansgawendowicz pascallenzner podc tobiasfriedrich year2023},
  title = {The Impact of Cooperation in Bilateral Network Creation},
  year = 2023
}

Clean Citation Style 005

Angrick, Sebastian; Bals, Ben; Casel, Katrin; Cohen, Sarel; Friedrich, Tobias; Hastrich, Niko; Hradilak, Theresa; Issac, Davis; Kißig, Otto; Schmidt, Jonas; Wendt, Leo Solving Directed Feedback Vertex Set by Iterative Reduction to Vertex CoverSymposium on Experimental Algorithms (SEA) 2023: 10:1–10:14

[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]

Clean Citation Style 005

Casel, Katrin; Friedrich, Tobias; Schirneck, Martin; Wietheger, Simon Fair Correlation Clustering in ForestsFoundations of Responsible Computing (FORC) 2023: 9:1–9:12

[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]

The study of algorithmic fairness received growing attention recently. This stems from the awareness that bias in the input data for machine learning systems may result in discriminatory outputs. For clustering tasks, one of the most central notions of fairness is the formalization by Chierichetti, Kumar, Lattanzi, and Vassilvitskii [NeurIPS 2017]. A clustering is said to be fair, if each cluster has the same distribution of manifestations of a sensitive attribute as the whole input set. This is motivated by various applications where the objects to be clustered have sensitive attributes that should not be over- or underrepresented. Most research on this version of fair clustering has focused on centriod-based objectives. In contrast, we discuss the applicability of this fairness notion to Correlation Clustering. The existing literature on the resulting Fair Correlation Clustering problem either presents approximation algorithms with poor approximation guarantees or severely limits the possible distributions of the sensitive attribute (often only two manifestations with a 1:1 ratio are considered). Our goal is to understand if there is hope for better results in between these two extremes. To this end, we consider restricted graph classes which allow us to characterize the distributions of sensitive attributes for which this form of fairness is tractable from a complexity point of view. While existing work on Fair Correlation Clustering gives approximation algorithms, we focus on exact solutions and investigate whether there are efficiently solvable instances. The unfair version of Correlation Clustering is trivial on forests, but adding fairness creates a surprisingly rich picture of complexities. We give an overview of the distributions and types of forests where Fair Correlation Clustering turns from tractable to intractable. As the most surprising insight, we consider the fact that the cause of the hardness of Fair Correlation Clustering is not the strictness of the fairness condition. We lift most of our results to also hold for the relaxed version of the fairness condition. Instead, the source of hardness seems to be the distribution of the sensitive attribute. On the positive side, we identify some reasonable distributions that are indeed tractable. While this tractability is only shown for forests, it may open an avenue to design reasonable approximations for larger graph classes.

@inproceedings{case2023correlation,
  abstract = {The study of algorithmic fairness received growing attention recently. This stems from the awareness that bias in the input data for machine learning systems may result in discriminatory outputs. For clustering tasks, one of the most central notions of fairness is the formalization by Chierichetti, Kumar, Lattanzi, and Vassilvitskii [NeurIPS 2017]. A clustering is said to be fair, if each cluster has the same distribution of manifestations of a sensitive attribute as the whole input set. This is motivated by various applications where the objects to be clustered have sensitive attributes that should not be over- or underrepresented. Most research on this version of fair clustering has focused on centriod-based objectives. In contrast, we discuss the applicability of this fairness notion to Correlation Clustering. The existing literature on the resulting Fair Correlation Clustering problem either presents approximation algorithms with poor approximation guarantees or severely limits the possible distributions of the sensitive attribute (often only two manifestations with a 1:1 ratio are considered). Our goal is to understand if there is hope for better results in between these two extremes. To this end, we consider restricted graph classes which allow us to characterize the distributions of sensitive attributes for which this form of fairness is tractable from a complexity point of view. While existing work on Fair Correlation Clustering gives approximation algorithms, we focus on exact solutions and investigate whether there are efficiently solvable instances. The unfair version of Correlation Clustering is trivial on forests, but adding fairness creates a surprisingly rich picture of complexities. We give an overview of the distributions and types of forests where Fair Correlation Clustering turns from tractable to intractable. As the most surprising insight, we consider the fact that the cause of the hardness of Fair Correlation Clustering is not the strictness of the fairness condition. We lift most of our results to also hold for the relaxed version of the fairness condition. Instead, the source of hardness seems to be the distribution of the sensitive attribute. On the positive side, we identify some reasonable distributions that are indeed tractable. While this tractability is only shown for forests, it may open an avenue to design reasonable approximations for larger graph classes.},
  author = {Casel, Katrin and Friedrich, Tobias and Schirneck, Martin and Wietheger, Simon},
  booktitle = {Foundations of Responsible Computing (FORC)},
  keywords = {forc katrincasel martinschirneck simonwietheger tobiasfriedrich year2023},
  pages = {9:1-9:12},
  title = {Fair Correlation Clustering in Forests},
  year = 2023
}

Clean Citation Style 005

Bilò, Davide; Choudhary, Keerti; Cohen, Sarel; Friedrich, Tobias; Krogmann, Simon; Schirneck, Martin Compact Distance Oracles with Large Sensitivity and Low StretchAlgorithms and Data Structures Symposium (WADS) 2023: 149–163

[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]

@inproceedings{bilo2023compact,
  abstract = {An \(f\)-edge fault-tolerant distance sensitive oracle (\(f\)-DSO) with stretch \(\sigma \geq 1\) is a data-structure that preprocesses an input graph \(G = (V,E)\). When queried with the triple \((s,t,F)\), where \(s, t \in V\) and \(F \subseteq E\) contains at most \(f\) edges of \(G\), the oracle returns an estimate \(\widehat{d}_{G-F}(s,t)\) of the distance \(d_{G-F}(s,t)\) between \(s\) and \(t\) in the graph \(G-F\) such that \(d_{G-F}(s,t) \leq \widehat{d}_{G-F}(s,t) \leq \sigma \cdot d_{G-F}(s,t)\). For any positive integer \(k \ge 2\) and any \(0 < \alpha < 1\), we present an \(f\)-DSO with sensitivity \(f = o(\log n/\log\log n)\), stretch \(2k-1\), space \(O(n^{1+\frac{1}{k}+\alpha+o(1)})\), and an \(\widetilde{O}(n^{1+\frac{1}{k} - \frac{\alpha}{k(f+1)}})\) query time. Prior to our work, there were only three known \(f\)-DSOs with subquadratic space. The first one by Chechik et al. [Algorithmica 2012] has a stretch of \((8k-2)(f+1)\), depending on \(f\). Another approach is storing an \(f\)-edge fault-tolerant \((2k-1)\)-spanner of \(G\). The bottleneck is the large query time due to the size of any such spanner, which is \(\Omega(n^{1+1/k})\) under the Erdős girth conjecture. Bilò et al. [STOC 2023] gave a solution with stretch \(3+\varepsilon\), query time \(O(n^{\alpha})\) but space \(O(n^{2-\frac{\alpha}{f+1}})\), approaching the quadratic barrier for large sensitivity. In the realm of subquadratic space, our \(f\)-DSOs are the first ones that guarantee, at the same time, large sensitivity, low stretch, and non-trivial query time. To obtain our results, we use the approximate distance oracles of Thorup and Zwick [JACM 2005], and the derandomization of the \(f\)-DSO of Weimann and Yuster [TALG 2013] that was recently given by Karthik and Parter [SODA 2021].},
  author = {Bilò, Davide and Choudhary, Keerti and Cohen, Sarel and Friedrich, Tobias and Krogmann, Simon and Schirneck, Martin},
  booktitle = {Algorithms and Data Structures Symposium (WADS)},
  keywords = {davidebilo keertichoudhary martinschirneck sarelcohen simonkrogmann tobiasfriedrich wads year2023},
  pages = {149-163},
  title = {Compact Distance Oracles with Large Sensitivity and Low Stretch},
  year = 2023
}

Bandyapadhyay, Sayan; Fomin, Fedor V.; Inamdar, Tanmay; Panolan, Fahad; Simonov, Kirill Socially Fair Matching: Exact and Approximation AlgorithmsWorkshop on Algorithms and Data Structures (WADS) 2023: 79–92

[ Abstract ] [ BibTeX ] [ URL ] [ DOI ] [ Download ]

@inproceedings{bandyapadhyay2023socially,
  abstract = {Matching problems are some of the most well-studied problems in graph theory and combinatorial optimization, with a variety of theoretical as well as practical motivations. However, in many applications of optimization problems, a ``solution'' corresponds to real-life decisions that have major impact on humans belonging to diverse groups defined by attributes such as gender, race, or ethnicity. Due to this motivation, the notion of \emph{algorithmic fairness} has recently emerged to prominence. Depending on specific application, researchers have introduced several notions of fairness. In this paper, we study a problem called ``Socially Fair Matching'', which combines the traditional Minimum Weight Perfect Matching problem with the notion of social fairness that has been studied in clustering literature [Abbasi et al., and Ghadiri et al., FAccT, 2021]. In our problem, the input is an edge-weighted complete bipartite graph, where the bipartition represent two groups of entities. The goal is to find a perfect matching as well as an assignment that assigns the cost of each matched edge to one of its endpoints, such that the maximum of the total cost assigned to either of the two groups is minimized. Unlike Minimum Weight Perfect Matching, we show that Socially Fair Matching is weakly NP-hard. On the positive side, we design a deterministic PTAS for the problem when the edge weights are arbitrary. Furthermore, if the weights are integers and polynomial in the number of vertices, then we give a randomized polynomial-time algorithm that solves the problem exactly. Next, we show that this algorithm can be used to obtain a randomized FPTAS when the weights are arbitrary.},
  author = {Bandyapadhyay, Sayan and Fomin, Fedor V. and Inamdar, Tanmay and Panolan, Fahad and Simonov, Kirill},
  booktitle = {Workshop on Algorithms and Data Structures (WADS)},
  keywords = {sys:relevantfor:ae kirillsimonov wads year2023},
  pages = {79&ndash;92},
  title = {Socially Fair Matching: Exact and Approximation Algorithms},
  year = 2023
}