Abstract Given a set of agents qualifying or disqualifying each other, group identification is the task of identifying a socially qualified subgroup of agents. Social qualification depends on the specific rule used to aggregate individual qualifications . The classical bribery problem in this context asks how many agents need to change their qualifications in order to change the outcome in a certain way. Complementing previous results showing polynomial-time solvability or NP-hardness of bribery for various social rules in the constructive (aiming at making specific agents socially qualified) or destructive (aiming at making specific agents socially disqualified) setting, we provide a comprehensive picture of the parameterized computational complexity landscape. Conceptually, we also consider a more fine-grained concept of bribery cost, where we ask how many single qualifications need to be changed, nonunit prices for different bribery actions, and a more general bribery goal that combines the constructive and destructive setting.

Given an initial resource allocation, where some agents may envy others or where a different distribution of resources might lead to a higher social welfare, our goal is to improve the allocation without reassigning resources. We consider a sharing concept allowing resources being shared with social network neighbors of the resource owners. More precisely, our model allows agents to form pairs which then may share a limited number of resources. Sharing a resource can come at some costs or loss in utility. To this end, we introduce a formal model that allows a central authority to compute an optimal sharing between neighbors based on an initial allocation. Advocating this point of view, we focus on the most basic scenario where each agent can participate in a bounded number of sharings. We present algorithms for optimizing utilitarian and egalitarian social welfare of allocations and for reducing the number of envious agents. In particular, we examine the computational complexity with respect to several natural parameters. Furthermore, we study cases with restricted social network structures and, among others, devise polynomial-time algorithms in path- and tree-like (hierarchical) social networks.

Given an initial resource allocation, where some agents may envy others or where a different distribution of resources might lead to higher social welfare, our goal is to improve the allocation without reassigning resources. We consider a sharing concept allowing resources being shared with social network neighbors of the resource owners. To this end, we introduce a formal model that allows a central authority to compute an optimal sharing between neighbors based on an initial allocation. Advocating this point of view, we focus on the most basic scenario where a resource may be shared by two neighbors in a social network and each agent can participate in a bounded number of sharings. We present algorithms for optimizing utilitarian and egalitarian social welfare of allocations and for reducing the number of envious agents. In particular, we examine the computational complexity with respect to several natural parameters. Furthermore, we study cases with restricted social network structures and, among others, devise polynomial-time algorithms in path- and tree-like (hierarchical) social networks.

Abstract In this paper, we study the hybrid dual attack over learning with errors (LWE) problems for any secret distribution. Prior to our work, hybrid attacks are only considered for sparse and/or small secrets. A new and interesting result from our analysis shows that for most cryptographic use cases a hybrid dual attack outperforms a standalone dual attack, regardless of the secret distribution. We formulate our results into a framework of predicting the performance of the hybrid dual attacks. We also present a few tricks that further improve our attack. To illustrate the effectiveness of our result, we re-evaluate the security of all LWE related proposals in round 3 of NIST’s post-quantum cryptography process, and improve the state-of-the-art cryptanalysis results by 2-15 bits, under the BKZ-core-SVP model.

Abstract We introduce a dynamic version of the -hard graph modification problemCluster Editing. The essential point here is to take into account dynamically evolving input graphs: having a cluster graph (that is, a disjoint union of cliques) constituting a solution for a first input graph, can we cost-efficiently transform it into a “similar” cluster graph that is a solution for a second (“subsequent”) input graph? This model is motivated by several application scenarios, including incremental clustering, the search for compromise clusterings, or also local search in graph-based data clustering. We thoroughly study six problem variants (three modification scenarios edge editing, edge deletion, edge insertion; each combined with two distance measures between cluster graphs). We obtain both fixed-parameter tractability as well as (parameterized) hardness results, thus (except for three open questions) providing a fairly complete picture of the parameterized computational complexity landscape under the two perhaps most natural parameterizations: the distances of the new “similar” cluster graph to (1) the second input graph and to (2) the input cluster graph.

Abstract We study the -hard graph problemCollapsed k-Corewhere, given an undirected graphGand integersb,x, andk, we are asked to removebvertices such that thek-core of remaining graph, that is, the (uniquely determined) largest induced subgraph with minimum degreek, has size at mostx.Collapsed k-Corewas introduced by Zhang et al. (2017) and it is motivated by the study of engagement behavior of users in a social network and measuring the resilience of a network against user drop outs.Collapsed k-Coreis a generalization ofr-Degenerate Vertex Deletion(which is known to be -hard for allr≥ 0) where, given an undirected graphGand integersbandr, we are asked to removebvertices such that the remaining graph isr-degenerate, that is, every its subgraph has minimum degree at mostr. We investigate the parameterized complexity ofCollapsed k-Corewith respect to the parametersb,x, andk, and several structural parameters of the input graph. We reveal a dichotomy in the computational complexity ofCollapsed k-Corefork≤ 2 andk≥ 3. For the latter case it is known that for allx≥ 0Collapsed k-Coreis -hard when parameterized byb. Fork≤ 2 we show thatCollapsed k-Coreis -hard when parameterized byband in when parameterized by (b+x). Furthermore, we outline thatCollapsed k-Coreis in when parameterized by the treewidth of the input graph and presumably does not admit a polynomial kernel when parameterized by the vertex cover number of the input graph.

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”.

Given a set of individuals qualifying or disqualifying each other, group identification is the task of identifying a socially qualified subgroup of individuals. Social qualification depends on the specific rule used to aggregate individual qualifications. The bribery problem in this context asks how many agents need to change their qualifications in order to change the outcome. Complementing previous results showing polynomial-time solvability or NP-hardness of bribery for various social rules in the constructive (aiming at making specific individuals socially qualified) or destructive (aiming at making specific individuals socially disqualified) setting, we provide a comprehensive picture of the parameterized computational complexity landscape. Conceptually, we also consider a more fine-grained concept of bribery cost, where we ask how many single qualifications need to be changed, and a more general bribery goal that combines the constructive and destructive setting.

We introduce a dynamic version of the NP-hard Cluster Editing problem. The essential point here is to take into account dynamically evolving input graphs: Having a cluster graph (that is, a disjoint union of cliques) that represents a solution for a first input graph, can we cost-efficiently transform it into a "similar" cluster graph that is a solution for a second ("subsequent") input graph? This model is motivated by several application scenarios, including incremental clustering, the search for compromise clusterings, or also local search in graph-based data clustering. We thoroughly study six problem variants (edge editing, edge deletion, edge insertion; each combined with two distance measures between cluster graphs). We obtain both fixed-parameter tractability as well as parameterized hardness results, thus (except for two open questions) providing a fairly complete picture of the parameterized computational complexity landscape under the perhaps two most natural parameterizations: the distance of the new "similar" cluster graph to (i) the second input graph and to (ii) the input cluster graph.