Yongjie Yang

Planar graph vertex partition for linear problem kernels

A simple partition of the vertex set of a graph is introduced to analyze kernels for planar graph problems in which vertices and edges not in a solution have small distance to the solution. This method directly leads to improved kernel sizes for several problems, without needing new reduction rules. Moreover, new kernelization algorithms are developed for Connected Vertex Cover, Edge Dominating Set, and Maximum Triangle Packing problems, further improving the kernel sizes for these problems. Highlights? We propose a vertex-partition method for deriving linear kernels for planar graph problems. ? We improve the linear kernel for Connected Vertex Cover on planar graphs from 14k to 4k. ? We improve the linear kernel for Edge Dominating Set on planar graphs from 28k to 12k. ? We improve the linear kernel for Maximum Triangle Packing on planar graphs from 624k to 75k.

The control complexity of r-Approval: From the single-peaked case to the general case☆

A natural generalization of the single-peaked elections is the k-peaked elections, where at most k peaks are allowed in each vote. Motivated by NP-hardness in general and polynomial-time solvability in single-peaked elections, we aim at establishing a complexity dichotomy of several control problems for r-Approval voting in k-peaked elections with respect to k. It turns out that most NP-completeness results in general also hold in k-peaked elections, even for k=2,3. On the other hand, we derive polynomial-time algorithms for certain control problems for k=2. In addition, we also study the problems from the viewpoint of parameterized complexity and achieve both FPT and W-hardness results. Several of our results apply to approval voting and sincere-strategy preference-based approval voting as well.

Possible Winner Problems on Partial Tournaments: A Parameterized Study

We study possible winner problems related to uncovered set and Banks set on partial tournaments from the viewpoint of parameterized complexity. We first study the following problem, where given a partial tournament D and a subset X of vertices, we are asked to add some arcs to D such that all vertices in X are included in the uncovered set. Here we focus on two parameterizations of the problem: parameterized by |X| and parameterized by the number of arcs to be added to make all vertices of X be included in the uncovered set. In addition, we study a parameterized variant of the problem to decide whether we can make all vertices of X be included in the uncovered set by reversing at most k arcs. Finally, we study some parameterizations of a possible winner problem on partial tournaments, where we are given a partial tournament D and a distinguished vertex p, and asked whether D has a maximal transitive subtournament with p being the 0-indegree vertex. These parameterized problems are related to Banks set. For all these parameterized problems studied in this paper, we achieve

Linear problem kernels for planar graph problems with small distance property

\mathcal{XP}

How hard is it to control a group

results,

Possible winner problems on partial tournaments: a parameterized study

\mathcal{W}

Exact algorithms for weighted and unweighted Borda manipulation problems

-hardness results as well as

Complexity of Group Identification with Partial Information

\mathcal{FPT}

Kernelization of Two Path Searching Problems on Split Graphs

results along with a kernelization lower bound.

On the complexity of bribery with distance restrictions

Recently, various linear problem kernels for NP-hard planar graph problems have been achieved, finally resulting in a meta-theorem for classification of problems admitting linear kernels. Almost all of these results are based on a so-called region decomposition technique. In this paper, we introduce a simple partition of the vertex set to analyze kernels for planar graph problems which admit the distance property with small constants. Without introducing new reduction rules, this vertex partition directly leads to improved kernel sizes for several problems. Moreover, we derive new kernelization algorithms for Connected Vertex Cover, Edge Dominating Set, and Maximum Triangle Packing problems, further improving the kernel size upper bounds for these problems.