In varied real-life situations, ranging from carpooling to workload delegation, several activitie... more In varied real-life situations, ranging from carpooling to workload delegation, several activities are to be performed, to which end each activity should be assigned to a group of agents. These situations are captured by the Group Activity Selection Problem (GASP). Notably, relevant relations among agents, such as acquaintanceship or physical distance, can often be modeled naturally using graphs. To exploit this modeling ability, Igarashi, Peters and Elkind [AAAI 17] introduced gGASP. Specifically, it is required that each group would correspond to a connected set of the underlying graph. In addition, to enforce the execution of the activities in practice, no individual should desire to desert its group in favor of joining another group. In other words, the assignment should be Nash stable. In this paper, we study gGASP with Nash stability (gNSGA), whose objective is to compute such an assignment. This problem is computationally hard even on such restricted topologies as paths and stars, which naturally led Igarashi, Bredereck, Peters and Elkind [AAAI 17, AAMAS 17] to the study gNSGA in the framework of parameterized complexity. We take this line of investigation forward, significantly advancing the state-of-the-art. First, we show that gNSGA is NP-hard even when merely one activity is present. In fact, this special case remains NP-hard when we further restrict the graph to have maximum degree \(\varDelta =5\). Consequently, gNSGA is not fixed-parameter tractable (FPT), or even XP, when parameterized by \(p+\varDelta \), where p is the number of activities. However, we are able to design a parameterized algorithm for gNSGA on general graphs with respect to \(p+\varDelta +t\), where t is the maximum size of a group. Finally, we develop an algorithm that solves gNSGA on graphs of bounded treewidth \(\mathbf {tw}\) in time \(4^p\cdot (n\,+\,p)^{\mathcal {O}(\mathbf {tw})}\). Here, \(\varDelta +t\) can be arbitrarily large. Along the way, we resolve several open questions regarding gNSGA.
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, 2018
In a tournament, $n$ players enter the competition. In each round, they are paired-up to compete ... more In a tournament, $n$ players enter the competition. In each round, they are paired-up to compete against each other. Losers are thrown, while winners proceed to the next round, until only one player (the winner) is left. Given a prediction of the outcome, for every pair of players, of a match between them (modeled by a digraph $D$), the competitive nature of a tournament makes it attractive for manipulators. In the Tournament Fixing (TF) problem, the goal is to decide if we can conduct the competition (by controlling how players are paired-up) so that our favorite player $w$ wins. A common form of manipulation is to bribe players to alter the outcome of matches. Kim and Williams [IJCAI 2015] integrated such deceit into TF, and showed that the resulting problem is NP-hard when $\ell<(1-\epsilon)\log n$ alterations are possible (for any fixed $\epsilon>0$). For this problem, our contribution is fourfold. First, we present two operations that ``obfuscate deceit'': given o...
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, 2018
A knockout tournament is a standard format of competition, ubiquitous in sports, elections and de... more A knockout tournament is a standard format of competition, ubiquitous in sports, elections and decision making. Such a competition consists of several rounds. In each round, all players that have not yet been eliminated are paired up into matches. Losers are eliminated, and winners are raised to the next round, until only one winner exists. Given that we can correctly predict the outcome of each potential match (modelled by a tournament D), a seeding of the tournament deterministically determines its winner. Having a favorite player v in mind, the Tournament Fixing Problem (TFP) asks whether there exists a seeding that makes v the winner. Aziz et al. [AAAI’14] showed that TFP is NP-hard. They initiated the study of the parameterized complexity of TFP with respect to the feedback arc set number k of D, and gave an XP-algorithm (which is highly inefficient). Recently, Ramanujan and Szeider [AAAI’17] showed that TFP admits an FPT algorithm, running in time 2^{ O(k^2 log k)} n ^{O(1)}. ...
Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, 2021
We study generalizations of stable matching in which agents may be matched fractionally; this mod... more We study generalizations of stable matching in which agents may be matched fractionally; this models time-sharing assignments. We focus on the so-called ordinal stability and cardinal stability, and investigate the computational complexity of finding an ordinally stable or cardinally stable fractional matching which either maximizes the social welfare (i.e., the overall utilities of the agents) or the number of fully matched agents (i.e., agents whose matching values sum up to one). We complete the complexity classification of both optimization problems for both ordinal stability and cardinal stability, distinguishing between the marriage (bipartite) and roommates (non-bipartite) cases and the presence or absence of ties in the preferences. In particular, we prove a surprising result that finding a cardinally stable fractional matching with maximum social welfare is NP-hard even for the marriage case without ties. This answers an open question and exemplifies a rare variant of stabl...
In varied real-life situations, ranging from carpooling to workload delegation, several activitie... more In varied real-life situations, ranging from carpooling to workload delegation, several activities are to be performed, to which end each activity should be assigned to a group of agents. These situations are captured by the Group Activity Selection Problem (GASP). Notably, relevant relations among agents, such as acquaintanceship or physical distance, can often be modeled naturally using graphs. To exploit this modeling ability, Igarashi, Peters and Elkind [AAAI 17] introduced gGASP. Specifically, it is required that each group would correspond to a connected set of the underlying graph. In addition, to enforce the execution of the activities in practice, no individual should desire to desert its group in favor of joining another group. In other words, the assignment should be Nash stable. In this paper, we study gGASP with Nash stability (gNSGA), whose objective is to compute such an assignment. This problem is computationally hard even on such restricted topologies as paths and stars, which naturally led Igarashi, Bredereck, Peters and Elkind [AAAI 17, AAMAS 17] to the study gNSGA in the framework of parameterized complexity. We take this line of investigation forward, significantly advancing the state-of-the-art. First, we show that gNSGA is NP-hard even when merely one activity is present. In fact, this special case remains NP-hard when we further restrict the graph to have maximum degree \(\varDelta =5\). Consequently, gNSGA is not fixed-parameter tractable (FPT), or even XP, when parameterized by \(p+\varDelta \), where p is the number of activities. However, we are able to design a parameterized algorithm for gNSGA on general graphs with respect to \(p+\varDelta +t\), where t is the maximum size of a group. Finally, we develop an algorithm that solves gNSGA on graphs of bounded treewidth \(\mathbf {tw}\) in time \(4^p\cdot (n\,+\,p)^{\mathcal {O}(\mathbf {tw})}\). Here, \(\varDelta +t\) can be arbitrarily large. Along the way, we resolve several open questions regarding gNSGA.
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, 2018
In a tournament, $n$ players enter the competition. In each round, they are paired-up to compete ... more In a tournament, $n$ players enter the competition. In each round, they are paired-up to compete against each other. Losers are thrown, while winners proceed to the next round, until only one player (the winner) is left. Given a prediction of the outcome, for every pair of players, of a match between them (modeled by a digraph $D$), the competitive nature of a tournament makes it attractive for manipulators. In the Tournament Fixing (TF) problem, the goal is to decide if we can conduct the competition (by controlling how players are paired-up) so that our favorite player $w$ wins. A common form of manipulation is to bribe players to alter the outcome of matches. Kim and Williams [IJCAI 2015] integrated such deceit into TF, and showed that the resulting problem is NP-hard when $\ell<(1-\epsilon)\log n$ alterations are possible (for any fixed $\epsilon>0$). For this problem, our contribution is fourfold. First, we present two operations that ``obfuscate deceit'': given o...
Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, 2018
A knockout tournament is a standard format of competition, ubiquitous in sports, elections and de... more A knockout tournament is a standard format of competition, ubiquitous in sports, elections and decision making. Such a competition consists of several rounds. In each round, all players that have not yet been eliminated are paired up into matches. Losers are eliminated, and winners are raised to the next round, until only one winner exists. Given that we can correctly predict the outcome of each potential match (modelled by a tournament D), a seeding of the tournament deterministically determines its winner. Having a favorite player v in mind, the Tournament Fixing Problem (TFP) asks whether there exists a seeding that makes v the winner. Aziz et al. [AAAI’14] showed that TFP is NP-hard. They initiated the study of the parameterized complexity of TFP with respect to the feedback arc set number k of D, and gave an XP-algorithm (which is highly inefficient). Recently, Ramanujan and Szeider [AAAI’17] showed that TFP admits an FPT algorithm, running in time 2^{ O(k^2 log k)} n ^{O(1)}. ...
Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, 2021
We study generalizations of stable matching in which agents may be matched fractionally; this mod... more We study generalizations of stable matching in which agents may be matched fractionally; this models time-sharing assignments. We focus on the so-called ordinal stability and cardinal stability, and investigate the computational complexity of finding an ordinally stable or cardinally stable fractional matching which either maximizes the social welfare (i.e., the overall utilities of the agents) or the number of fully matched agents (i.e., agents whose matching values sum up to one). We complete the complexity classification of both optimization problems for both ordinal stability and cardinal stability, distinguishing between the marriage (bipartite) and roommates (non-bipartite) cases and the presence or absence of ties in the preferences. In particular, we prove a surprising result that finding a cardinally stable fractional matching with maximum social welfare is NP-hard even for the marriage case without ties. This answers an open question and exemplifies a rare variant of stabl...
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Papers by Sanjukta Roy