Abstract Sequential voting rules have played a crucial role in shaping decisions within parliamentary and legislative frameworks. After observing that the existing sequential rules fail several fundamental axioms, (Horan and Sprumont, Theoretical Economics, 17(2), 521–537 2022) proposed a sequential rule named two-stage majoritarian rule (TSMR). This paper examines this rule by investigating the complexity of Agenda Control , Coalition Manipulation , Possible Winner , Necessary Winner , and eight standard election control problems. Our study offers a comprehensive insight into the complexity landscape of these problems.

Abstract This paper studies the complexity of two microbribery problems under the model of group identification. In these problems, we are given a subset of distinguished individuals, and the questions are whether these individuals can be made socially qualified or whether they can be made exactly the socially qualified individuals, respectively, by modifying a limited number of entries in the qualifications-profile. For consent rules, the consensus-start-respecting rule, and the liberal-start-respecting rule, we obtain many NP-hardness results and polynomial-time solvability results. We also study the problems in r-profiles where each individual qualifies exactly r individuals.

Abstract The amendment procedure and the successive procedure have been widely employed in parliamentary and legislative decision making and have undergone extensive study in the literature from various perspectives. However, investigating them through the lens of computational complexity theory has not been as thoroughly conducted as for many other prevalent voting procedures heretofore. To the best of our knowledge, there is only one paper which explores the complexity of several strategic voting problems under these two procedures, prior to our current work. To provide a better understanding of to what extent the two procedures resist strategic behavior, we study the parameterized complexity of constructive/destructive control by adding/deleting voters/candidates for both procedures. To enhance the generalizability of our results, we also examine a more generalized form of the amendment procedure. Our exploration yields a comprehensive (parameterized) complexity landscape of these problems with respect to numerous parameters.

We study a graph partition problem where the input is a directed acyclic graph (DAG) representing tasks as vertices and dependencies between tasks as arcs. The goal is to assign the tasks to k heterogeneous machines in a way that minimizes the total energy consumed for completing the tasks. We first show that the problem is NP -hard. Then, we present polynomial-time algorithms for two special cases: one where there are only two machines, and another where the input DAG is a directed path. Finally, we examine a variant where there are only two machines, with one capable of executing a limited number of tasks, and demonstrate that this special case remains computationally hard.

Abstract We consider GROUP CONTROL BY ADDING INDIVIDUALS (GCAI) in the setting of group identification for two procedural rules—the consensus-start-respecting rule and the liberal-start-respecting rule. It is known that GCAI for both rules are NP-hard, but whether they are fixed-parameter tractable with respect to the number of distinguished individuals remained open. We resolve both open problems in the affirmative. In addition, we strengthen the NP-hardness of GCAI by showing that, with respect to the natural parameter the number of added individuals, GCAI for both rules are W[2]-hard. Notably, the W[2]-hardness for the liberal-start-respecting rule holds even when restricted to a very special case where the qualifications of individuals satisfy the so-called consecutive ones property. However, for the consensus-start-respecting rule, the problem becomes polynomial-time solvable in this special case. We also study a dual restriction where the disqualifications of individuals fulfill the consecutive ones property, and show that under this restriction GCAI for both rules turn out to be polynomial-time solvable. Our reductions for showing W[2]-hardness also imply several algorithmic lower bounds.

Abstract We study the parameterized complexity of winner determination problems for three prevalent k-committee selection rules, namely the minimax approval voting (MAV), the proportional approval voting (PAV), and the Chamberlin–Courant’s approval voting (CCAV). It is known that these problems are computationally hard. Although they have been studied from the parameterized complexity point of view with respect to several natural parameters, many of them turned out to be -hard or -hard. Aiming at obtaining plentiful fixed-parameter algorithms, we revisit these problems by considering more natural single parameters, combined parameters, and structural parameters.

We study approval-based multiwinner voting where candidates are in a metric space and committees are valuated in terms of their distances to the given votes. In particular, we consider three different distance functions, and for each of them we study both the utilitarian rules and the egalitarian rules, resulting in six variants of winners determination problems. We focus on the (parameterized) complexity of these problems for both the general metric and several special metrics. For hardness results, we also discuss their approximability.

We propose a model of winners allocation. In this model, we are given are two elections where the sets of candidates may intersect. The goal is to find two disjoint winning committees from respectively the two elections that are subjected to certain reasonable restrictions. For our model, we first propose several desirable properties. Then, we investigate the implication relationships among these properties. Finally, we study the complexity of computing winners allocations providing these properties. For hardness results, we also study some fixed-parameter algorithms.

Abstract We investigate the computational complexity of electoral control in elections. Electoral control describes the scenario where the election chair seeks to alter the outcome of the election by structural changes such as adding, deleting, or replacing either candidates or voters. Such control actions have been studied in the literature for a lot of prominent voting rules. We complement those results by solving several open cases for Copeland $$^{\alpha }$$ α , maximin,k-veto, plurality with runoff, veto with runoff, Condorcet, fallback, range voting, and normalized range voting.

In 1990, Hendry conjectured that all Hamiltonian chordal graphs are cycle extendable. After a series of papers confirming the conjecture for a number of graph classes, the conjecture is yet refuted by Lafond and Seamone in 2015. Given that their counterexamples are not strongly chordal graphs and they are all only 2-connected, Lafond and Seamone asked the following two questions: (1) Are Hamiltonian strongly chordal graphs cycle extendable? (2) Is there an integer $k$ such that all $k$-connected Hamiltonian chordal graphs are cycle extendable? Later, a conjecture stronger than Hendry's is proposed. In this paper, we resolve all these questions in the negative. On the positive side, we add to the list of cycle-extendable graphs two more graph classes, namely, Hamiltonian 4-fan-free chordal graphs, where every induced $K_5 - e$ has true twins, and Hamiltonian $\{4{\sc -fan}, \overline{A} \}$-free chordal graphs.

We investigate the complexity of {\sc{Constructive Control by Adding/Deleting Votes}} (CCAV/CCDV) for $r$-approval, Condorcet, Maximin and Copeland$^{\alpha}$ in $k$-axes and $k$-candidates partition single-peaked elections. In general, we prove that CCAV and CCDV for most of the voting correspondences mentioned above are NP-hard even when~$k$ is a very small constant. Exceptions are CCAV and CCDV for Condorcet and CCAV for $r$-approval in $k$-axes single-peaked elections, which we show to be fixed-parameter tractable with respect to~$k$. In addition, we give a polynomial-time algorithm for recognizing $2$-axes elections, resolving an open problem. Our work leads to a number of dichotomy results. To establish an NP-hardness result, we also study a property of $3$-regular bipartite graphs which may be of independent interest. In particular, we prove that for every $3$-regular bipartite graph, there are two linear orders of its vertices such that the two endpoints of every edge are consecutive in at least one of the two orders.

As a successful application of edge computing in the industrial production environment, prolonging the smart devices' (SDs') battery lifetime has become an important issue. In some special practical applications, the uploaded data from SDs to vehicle base stations (VBSs) or servers can be merged between SDs with a fixed size, which is called superposed data. In this article, we consider the superposed data uploading problem in a decentralized device-to-device communication system. The task of the problem is to minimize the total energy consumption of uploading data. We reduce it into a combinatorial optimization problem from the graph theory perspective. For VBSs or servers with infinite capacities, we propose an optimal algorithm with polynomial running time. When VBSs or servers have limited capacities, the problem is NP-hard even in very special cases. For this NP-hard problem, we give two heuristic algorithms and the corresponding numerical simulation results.

We study the Maximum Satisfiability problem (MaxSAT). Particularly, we derive a branching algorithm of running time O*(1.2989^m) for the MaxSAT problem, where m denotes the number of clauses in the given CNF formula. Our algorithm considerably improves the previous best result O*(1.3248^m) by Chen and Kanj [2004] published 15 years ago. For our purpose, we derive improved branching strategies for variables of degrees 3, 4, and 5. The worst case of our branching algorithm is at variables of degree 4 which occur twice both positively and negatively in the given CNF formula. To serve the branching rules and shrink the size of the CNF formula, we also propose a variety of reduction rules which can be exhaustively applied in polynomial time and, moreover, some of them solve a bottleneck of the previous best algorithm.

We study the complexity of several manipulation and control problems for six prevalent approval based multiwinner voting rules. We show that these rules generally resist the proposed strategic types. In addition, we also give fixed-parameter tractability results for these problems with respect to several natural parameters and derive polynomial-time algorithms for certain special cases.

We study numerous restricted domains of dichotomous preferences with respect to some tree structures. Particularly, we study the relationships among these domains and the ones proposed by Elkind and Lackner [2015]. We also show that recognizing all the restricted domains proposed in this paper is polynomial-time solvable. Finally, we explore the complexity of winner determination for several important approval-based multiwinner voting rules when restricted to these domains.

Multiwinner voting aims to select a subset of candidates (the winners) from admissible sets, according to the votes cast by voters. A special class of multiwinner rules—the k-committee selection rules where the number of winners is predefined—have gained considerable attention recently. In this setting, the admissible sets are all subsets of candidates of size exactly k. In this paper, we study admissible sets with combinatorial restrictions. In particular, in our setting, we are given a graph G whose vertex set is the candidate set. Admissible sets are the subsets of candidates whose induced subgraphs belong to some special class G of graphs. We consider different graph classes G and investigate the complexity of multiwinner determination problem for prevalent voting rules in this setting. In addition, we investigate the strategyproofness of many rules for different classes of admissible sets.

We study the complexity of the bribery problem with distance restrictions. In particular, in the bribery problem, we are given an election and a distinguished candidate p, and are asked whether we can make p win/not win the election by bribing at most k voters to recast their votes. In the bribery problem with distance restrictions, we require that the votes recast by the bribed voters are close to their original votes. To measure the closeness between two votes, we adopt the prevalent Kendall-Tau distance and the Hamming distance. We achieve a wide range of complexity results for this problem under a variety of voting correspondences, including the Borda, Condorcet, Copelandαfor every 0≤α≤1 and Maximin.

We investigate the parameterized complexity of strategic behaviors in generalized scoring rules. In particular, we prove that the manipulation, control (all the 22 standard types), and bribery problems are fixed-parameter tractable for many generalized scoring rules, with respect to the number of candidates. Our results imply that all these strategic problems are fixed-parameter tractable for many common voting rules, such as Plurality, r-Approval, Borda, Copeland, Maximin, Bucklin, Ranked pairs, Schulze, etc., with respect to the number of candidates.