15 research outputs found
Stable Roommate Problem with Diversity Preferences
In the multidimensional stable roommate problem, agents have to be allocated
to rooms and have preferences over sets of potential roommates. We study the
complexity of finding good allocations of agents to rooms under the assumption
that agents have diversity preferences [Bredereck et al., 2019]: each agent
belongs to one of the two types (e.g., juniors and seniors, artists and
engineers), and agents' preferences over rooms depend solely on the fraction of
agents of their own type among their potential roommates. We consider various
solution concepts for this setting, such as core and exchange stability, Pareto
optimality and envy-freeness. On the negative side, we prove that envy-free,
core stable or (strongly) exchange stable outcomes may fail to exist and that
the associated decision problems are NP-complete. On the positive side, we show
that these problems are in FPT with respect to the room size, which is not the
case for the general stable roommate problem. Moreover, for the classic setting
with rooms of size two, we present a linear-time algorithm that computes an
outcome that is core and exchange stable as well as Pareto optimal. Many of our
results for the stable roommate problem extend to the stable marriage problem.Comment: accepted to IJCAI'2
Collecting, Classifying, Analyzing, and Using Real-World Elections
We present a collection of real-world elections divided into
datasets from various sources ranging from sports competitions over music
charts to survey- and indicator-based rankings. We provide evidence that the
collected elections complement already publicly available data from the PrefLib
database, which is currently the biggest and most prominent source containing
real-world elections from datasets. Using the map of elections
framework, we divide the datasets into three categories and conduct an analysis
of the nature of our elections. To evaluate the practical applicability of
previous theoretical research on (parameterized) algorithms and to gain further
insights into the collected elections, we analyze different structural
properties of our elections including the level of agreement between voters and
election's distances from restricted domains such as single-peakedness. Lastly,
we use our diverse set of collected elections to shed some further light on
several traditional questions from social choice, for instance, on the number
of occurrences of the Condorcet paradox and on the consensus among different
voting rules
Adapting Stable Matchings to Forced and Forbidden Pairs
We introduce the problem of adapting a stable matching to forced and
forbidden pairs. Specifically, given a stable matching , a set of
forced pairs, and a set of forbidden pairs, we want to find a stable
matching that includes all pairs from , no pair from , and that is as
close as possible to . We study this problem in four classical stable
matching settings: Stable Roommates (with Ties) and Stable Marriage (with
Ties). As our main contribution, we develop an algorithmic technique to
"propagate" changes through a stable matching. This technique is at the core of
our polynomial-time algorithm for adapting Stable Roommates matchings to forced
pairs. In contrast to this, we show that the same problem for forbidden pairs
is NP-hard. However, our propagation technique allows for a fixed-parameter
tractable algorithm with respect to the number of forbidden pairs when both
forced and forbidden pairs are present. Moreover, we establish strong
intractability results when preferences contain ties
Rank Aggregation Using Scoring Rules
To aggregate rankings into a social ranking, one can use scoring systems such
as Plurality, Veto, and Borda. We distinguish three types of methods: ranking
by score, ranking by repeatedly choosing a winner that we delete and rank at
the top, and ranking by repeatedly choosing a loser that we delete and rank at
the bottom. The latter method captures the frequently studied voting rules
Single Transferable Vote (aka Instant Runoff Voting), Coombs, and Baldwin. In
an experimental analysis, we show that the three types of methods produce
different rankings in practice. We also provide evidence that sequentially
selecting winners is most suitable to detect the "true" ranking of candidates.
For different rules in our classes, we then study the (parameterized)
computational complexity of deciding in which positions a given candidate can
appear in the chosen ranking. As part of our analysis, we also consider the
Winner Determination problem for STV, Coombs, and Baldwin and determine their
complexity when there are few voters or candidates.Comment: 47 pages including appendi
Deepening the (Parameterized) Complexity Analysis of Incremental Stable Matching Problems
When computing stable matchings, it is usually assumed that the preferences
of the agents in the matching market are fixed. However, in many realistic
scenarios, preferences change over time. Consequently, an initially stable
matching may become unstable. Then, a natural goal is to find a matching which
is stable with respect to the modified preferences and as close as possible to
the initial one. For Stable Marriage/Roommates, this problem was formally
defined as Incremental Stable Marriage/Roommates by Bredereck et al. [AAAI
'20]. As they showed that Incremental Stable Roommates and Incremental Stable
Marriage with Ties are NP-hard, we focus on the parameterized complexity of
these problems. We answer two open questions of Bredereck et al. [AAAI '20]: We
show that Incremental Stable Roommates is W[1]-hard parameterized by the number
of changes in the preferences, yet admits an intricate XP-algorithm, and we
show that Incremental Stable Marriage with Ties is W[1]-hard parameterized by
the number of ties. Furthermore, we analyze the influence of the degree of
"similarity" between the agents' preference lists, identifying several
polynomial-time solvable and fixed-parameter tractable cases, but also proving
that Incremental Stable Roommates and Incremental Stable Marriage with Ties
parameterized by the number of different preference lists are W[1]-hard.Comment: Accepted to MFCS'2