Many techniques have been developed for itemset mining problems. Famous examples are mining frequent itemsets (Agrawal et al., 1993; Han et al., 2000), mining association rules (Agrawal et al., 1993; Szathmary et al., 2007), mining closed itemsets(Pasquier et al., 1999), mining high utility itemsets (Chan et al., 2003), etc. Most of these works have focused on improving the practical performance of the mining process, but few have conducted a theoretical analysis of the computational complexity of itemset mining problems. Wijsen and Meersman (1998) have proved that it is NPcomplete to decide whether there exists a valid quantitative rule. Angiulli et al. (2001) have proved that the problem of deciding whether there exists a non-redundant association rule of size at least k that is frequent and the problem of deciding whether there exists a non-redundant association rule of size at least k that is confident are both NPcomplete.

Task allocation has been a well studied problem. In most prior problem formulations, it is assumed that each task is associated with a unique set of resource requirements. In the scope of multi-robot task allocation problem, these requirements can be satisfied by a coalition of robots. In this paper, we introduce a more general formulation of multi-robot task allocation problem that allows more than one option for specifying the set of task requirements--satisfying any one of the options will satisfy the task. We referred to this new problem as the multi-robot task allocation problem with task variants. First, we theoretically show that this extension fortunately does not impact the complexity class, which is still NP-complete. For solution methods, we adapt two previous greedy methods for the task allocation problem without task variants to solve this new problem and analyze their effectiveness. In particular, we "flatten" the new problem to the problem without task variants, modify the previous methods to solve the flattened problem, and prove that the bounds still hold. Finally, we thoroughly evaluate these two methods along with a random baseline to demonstrate their efficacy for the new problem.

Many objectives can be achieved (or may be achieved more effectively) only by a group of agents executing a team plan. If a team plan fails, it is often of interest to determine what caused the failure, the degree of responsibility of each agent for the failure, and the degree of blame attached to each agent. We show how team plans can be represented in terms of structural equations, and then apply the definitions of causality introduced by Halpern [2015] and degree of responsibility and blame introduced by Chockler and Halpern [2004] to determine the agent(s) who caused the failure and what their degree of responsibility/blame is. We also prove new results on the complexity of computing causality and degree of responsibility and blame, showing that they can be determined in polynomial time for many team plans of interest.

The weight maximization problem (WMP) is the problem of finding the word of highest weight on a weighted finite state automaton (WFA). It is an essential question that emerges in many optimization problems in automata theory. Unfortunately, the general problem can be shown to be undecidable, whereas its bounded decisional version is NP-complete. Designing efficient algorithms that produce approximate solutions to the WMP in reasonable time is an appealing research direction that can lead to several new applications including formal verification of systems abstracted as WFAs. In particular, in combination with a recent procedure that translates a recurrent neural network into a weighted automaton, an algorithm for the WMP can be used to analyze and verify the network by exploiting the simpler and more compact automata model. In this work, we propose, implement and evaluate a metaheuristic based on genetic algorithms to approximate solutions to the WMP. We experimentally evaluate its performance on examples from the literature and show its potential on different applications.

Can deep neural networks learn to solve any task, and in particular problems of high complexity? This question attracts a lot of interest, with recent works tackling computationally hard tasks such as the traveling salesman problem and satisfiability. In this work we offer a different perspective on this question. Given the common assumption that $\textit{NP} \neq \textit{coNP}$ we prove that any polynomial-time sample generator for an $\textit{NP}$-hard problem samples, in fact, from an easier sub-problem. We empirically explore a case study, Conjunctive Query Containment, and show how common data generation techniques generate biased datasets that lead practitioners to over-estimate model accuracy. Our results suggest that machine learning approaches that require training on a dense uniform sampling from the target distribution cannot be used to solve computationally hard problems, the reason being the difficulty of generating sufficiently large and unbiased training sets.

Bigraphical Reactive Systems (BRSs) [14, 20] are a flexible and expressive meta-model for ubiquitous computation. System states are represented by bigraphs, which are compositional data structures describing at once both the locations and the logical connections of (possibly nested) components of a system. Like graph rewriting [25], the dynamic behaviour of a system is defined by a set of (parametric) reaction rules, which can modify a bigraph by replacing a redex with a reactum, possibly changing agents' positions and connections. BRSs have been successfully applied to the formalization of a broad variety of domain-specific calculi and models, from traditional programming languages to process calculi for concurrency and mobility, from context-aware systems to web-service orchestration languages, from business processes to systems biology; a non exhaustive list is [2,4,5,8,16,19]. Very recently bigraphs have been used in structure-aware agent-based computing for modelling the structure of the (physical) world where the agents operates (e.g., drones, robots, etc.) [21]. Beside their normative and expressive power, BRSs are appealing because they provide a range of interesting general results and tools, which can be readily instantiated with the specific model under scrutiny: simulation tools, systematic construction of compositional bisimulations [14], graphical editors [9], general model checkers [24], modular composition [23], stochastic extensions [15], etc. In this paper, we give an implementation for a crucial problem that virtually all these tools have to deal with, i.e., the matching a bigraph inside an agent. Roughly, this can be stated as follows: given R and A, we have to find (all, or some) C,D such that A C R D. Clearly this is required by any simulation tool (in order to apply a reaction rule, we have to match the redex inside the agent, and then replace it with the reactum), but also in other tools, e.g., for implementing "find&replace" in graphical editors, for occurrence checks in sortings [1] and model checkers, for refinements in architectural design tools, etc. 1

Studying complexity of various bribery problems has been one of the main research focus in computational social choice. In all the models of bribery studied so far, the briber has to pay every voter some amount of money depending on what the briber wants the voter to report and the briber has some budget at her disposal. Although these models successfully capture many real world applications, in many other scenarios, the voters may be unwilling to deviate too much from their true preferences. In this paper, we study the computational complexity of the problem of finding a preference profile which is as close to the true preference profile as possible and still achieves the briber's goal subject to budget constraints. We call this problem Optimal Bribery. We consider three important measures of distances, namely, swap distance, footrule distance, and maximum displacement distance, and resolve the complexity of the optimal bribery problem for many common voting rules. We show that the problem is polynomial time solvable for the plurality and veto voting rules for all the three measures of distance. On the other hand, we prove that the problem is NP-complete for a class of scoring rules which includes the Borda voting rule, maximin, Copeland$^\alpha$ for any $\alpha\in[0,1]$, and Bucklin voting rules for all the three measures of distance even when the distance allowed per voter is $1$ for the swap and maximum displacement distances and $2$ for the footrule distance even without the budget constraints (which corresponds to having an infinite budget). For the $k$-approval voting rule for any constant $k>1$ and the simplified Bucklin voting rule, we show that the problem is NP-complete for the swap distance even when the distance allowed is $2$ and for the footrule distance even when the distance allowed is $4$ even without the budget constraints.

We discuss the connection between computational social choice (comsoc) and computational complexity. We stress the work so far on, and urge continued focus on, two less-recognized aspects of this connection. Firstly, this is very much a two-way street: Everyone knows complexity classification is used in comsoc, but we also highlight benefits to complexity that have arisen from its use in comsoc. Secondly, more subtle, less-known complexity tools often can be very productively used in comsoc.

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 such an approach is vulnerable to a new kind of manipulation which was not present in the classical (where preferences are complete orders) world of voting. We call this attack "manipulative elicitation." More specifically, it may be possible to (partially) elicit the preferences of the agents in a way that makes some distinguished alternative win the election who may not be a winner if we elicit every preference completely. More alarmingly, we show that the related computational task is polynomial time solvable for a large class of voting rules which includes all scoring rules, maximin, Copeland α for every α ∈ [0,1], simplified Bucklin voting rules, etc. We then show that introducing a parameter per pair of alternatives which specifies the minimum number of partial preferences where this pair of alternatives must be comparable makes the related computational task of manipulative elicitation NP-complete for all common voting rules including a class of scoring rules which includes the plurality,  k -approval, k -veto, veto, and Borda voting rules, maximin, Copeland α for every α ∈ [0,1], and simplified Bucklin voting rules. Hence, in this work, we discover a fundamental vulnerability in using minimax regret based approach in partial preferential setting and propose a novel way to tackle it.

We propose a simple model of interaction for resource-conscious agents. The resources involved are expressed in fragments of Linear Logic. We investigate a few problems relevant to cooperative games, such as deciding whether a group of agents can form a coalition and act together in a way that satisfies all of them. In terms of solution concepts, we study the computational aspects of the core of a game. The main contributions are a formal link with the existing literature, and complexity results for several classes of models.