Related papers: Complexity of and Algorithms for Borda Manipulatio…
We show that the problem of finding an optimal stochastic 'blind' controller in a Markov decision process is an NP-hard problem. The corresponding decision problem is NP-hard, in PSPACE, and SQRT-SUM-hard, hence placing it in NP would imply…
The number partition problem is a well-known problem, which is one of 21 Karp's NP-complete problems \cite{karp}. The partition function is a boolean function that is equivalent to the number partition problem with number range restricted.…
We study the control complexity of fallback voting. Like manipulation and bribery, electoral control describes ways of changing the outcome of an election; unlike manipulation or bribery attempts, control actions---such as…
We survey results on the hardness of approximating combinatorial optimization problems.
The stable marriage and stable roommates problems have been extensively studied due to their high applicability in various real-world scenarios. However, it might happen that no stable solution exists, or stable solutions do not meet…
There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…
Many binary collective choice situations can be described as weighted simple voting games. We introduce weighted committee games to model decisions on an arbitrary number of alternatives in analogous fashion. We compare the effect of…
We consider a monopolist seller facing a single buyer with additive valuations over n heterogeneous, independent items. It is known that in this important setting optimal mechanisms may require randomization [HR12], use menus of infinite…
Classical results in voting theory show that strategic manipulation by voters is inevitable if a voting rule simultaneously satisfy certain desirable properties. Motivated by this, we study the relevant question of how often a voting rule…
Electoral control refers to attempts by an election's organizer ("the chair") to influence the outcome by adding/deleting/partitioning voters or candidates. The groundbreaking work of Bartholdi, Tovey, and Trick [BTT92] on (constructive)…
Consider elections where the set of candidates is partitioned into parties, and each party must nominate exactly one candidate. The Possible President problem asks whether some candidate of a given party can become the winner of the…
We consider the hardness of approximation of optimization problems from the point of view of definability. For many NP-hard optimization problems it is known that, unless P = NP, no polynomial-time algorithm can give an approximate solution…
We focus on a generalization of the classic Minisum approval voting rule, introduced by Barrot and Lang (2016), and referred to as Conditional Minisum (CMS), for multi-issue elections with preferential dependencies. Under this rule, voters…
Variational quantum algorithms are proposed to solve relevant computational problems on near term quantum devices. Popular versions are variational quantum eigensolvers and quantum ap- proximate optimization algorithms that solve ground…
In a recent breakthrough result, Balliu et al. [FOCS'19] proved a deterministic $\Omega(\min(\Delta,\log n /\log \log n))$-round and a randomized $\Omega(\min(\Delta,\log \log n/\log \log \log n))$-round lower bound for the complexity of…
Lu and Boutilier proposed a novel approach based on "minimax regret" to use classical score based voting rules in the setting where preferences can be any partial (instead of complete) orders over the set of alternatives. We show here that…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
In liquid democracy, each voter either votes herself or delegates her vote to some other voter. This gives rise to what is called a delegation graph. To decide the voters who eventually votes along with the subset of voters whose votes they…
We address the problem of minimal actuator placement in linear systems so that the volume of the set of states reachable with one unit or less of input energy is lower bounded by a desired value. First, following the recent work of…
Imagine we want to split a group of agents into teams in the most \emph{efficient} way, considering that each agent has their own preferences about their teammates. This scenario is modeled by the extensively studied \textsc{Coalition…