12 research outputs found
The Complexity of Repairing, Adjusting, and Aggregating of Extensions in Abstract Argumentation
We study the computational complexity of problems that arise in abstract
argumentation in the context of dynamic argumentation, minimal change, and
aggregation. In particular, we consider the following problems where always an
argumentation framework F and a small positive integer k are given.
- The Repair problem asks whether a given set of arguments can be modified
into an extension by at most k elementary changes (i.e., the extension is of
distance k from the given set).
- The Adjust problem asks whether a given extension can be modified by at
most k elementary changes into an extension that contains a specified argument.
- The Center problem asks whether, given two extensions of distance k,
whether there is a "center" extension that is a distance at most (k-1) from
both given extensions.
We study these problems in the framework of parameterized complexity, and
take the distance k as the parameter. Our results covers several different
semantics, including admissible, complete, preferred, semi-stable and stable
semantics
Runtime analysis of randomized search heuristics for dynamic graph coloring
We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical graph coloring problem and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. This includes the (1+1) EA and RLS in a setting where the number of colors is bounded and we are minimizing the number of conflicts as well as iterated local search algorithms that use an unbounded color palette and aim to use the smallest colors and - as a consequence - the smallest number of colors.
We identify classes of bipartite graphs where reoptimization is as hard as or even harder than optimization from scratch, i. e. starting with a random initialization. Even adding a single edge can lead to hard symmetry problems. However, graph classes that are hard for one algorithm turn out to be easy for others. In most cases our bounds show that reoptimization is faster than optimizing from scratch. Furthermore, we show how to speed up computations by using problem specific operators concentrating on parts of the graph where changes have occurred
Adapting Stable Matchings to Evolving Preferences
Adaptivity to changing environments and constraints is key to success in
modern society. We address this by proposing "incrementalized versions" of
Stable Marriage and Stable Roommates. That is, we try to answer the following
question: for both problems, what is the computational cost of adapting an
existing stable matching after some of the preferences of the agents have
changed. While doing so, we also model the constraint that the new stable
matching shall be not too different from the old one. After formalizing these
incremental versions, we provide a fairly comprehensive picture of the
computational complexity landscape of Incremental Stable Marriage and
Incremental Stable Roommates. To this end, we exploit the parameters "degree of
change" both in the input (difference between old and new preference profile)
and in the output (difference between old and new stable matching). We obtain
both hardness and tractability results, in particular showing a fixed-parameter
tractability result with respect to the parameter "distance between old and new
stable matching".Comment: Accepted to AAAI 202
Time complexity analysis of randomized search heuristics for the dynamic graph coloring problem
We contribute to the theoretical understanding of randomized search heuristics for dynamic problems. We consider the classical vertex coloring problem on graphs and investigate the dynamic setting where edges are added to the current graph. We then analyze the expected time for randomized search heuristics to recompute high quality solutions. The (1+1) Evolutionary Algorithm and RLS operate in a setting where the number of colors is bounded and we are minimizing the number of conflicts. Iterated local search algorithms use an unbounded color palette and aim to use the smallest colors and, consequently, the smallest number of colors. We identify classes of bipartite graphs where reoptimization is as hard as or even harder than optimization from scratch, i.e., starting with a random initialization. Even adding a single edge can lead to hard symmetry problems. However, graph classes that are hard for one algorithm turn out to be easy for others. In most cases our bounds show that reoptimization is faster than optimizing from scratch. We further show that tailoring mutation operators to parts of the graph where changes have occurred can significantly reduce the expected reoptimization time. In most settings the expected reoptimization time for such tailored algorithms is linear in the number of added edges. However, tailored algorithms cannot prevent exponential times in settings where the original algorithm is inefficient