Multi-agent path planning is a challenging problem with numerous real-life applications, including robotics, logistics, military operations planning, disaster rescue, and computer games. We look at navigating large numbers of mobile units to their targets on navigation graphs such as grid maps. The size of problems examined is significantly larger than can be handled using optimal multi-agent pathfinding algorithms in practice. We introduced MAPP, a tractable algorithm for multi-agent path planning on undirected graphs. MAPP and its extended versions are complete on well specified and tractably testable classes of problems. They have low-polynomial worst-case upper bounds for the running time, the memory requirements, and the length of solutions. Experiments on realistic game grid maps, with uniformly randomly generated start and target locations for each unit, show MAPP as a state-of-the-art multi-agent pathfinding algorithm in terms of scalability and success ratio (i.e., percentage of solved units). Even on challenging scenarios with 2000 units, MAPP solves 92% to 99.7% of units. FAR and WHCA*, two fast but incomplete algorithms that were previously state-of-the-art in terms of scalability, solve as few as 17.5% and 12.3% of these problems. The quality of MAPP's solutions is empirically analyzed using multiple quality criteria: total travel distance, makespan, and sum of actions (including move and wait actions). MAPP is competitive in terms of solution quality and speed with FAR and WHCA*. MAPP further provides the formal characterizations that FAR and WHCA* lack, on problems it can solve as well as low-polynomial upper bounds on the resources required. As optimal algorithms have limited scalability, we evaluated the solution quality of suboptimal algorithms using lower bounds of optimal values. We showed that MAPP's solutions have a reasonable quality. For example, MAPP's total travel distance is on average 19% longer than a lower bound on the optimal value.

Thanks to the idea of social collaboration, Wikipedia has accumulated vast amount of semi-structured knowledge in which the link structure reflects human's cognition on semantic relationship to some extent. In this paper, we proposed a novel method RCRank to jointly compute concept-concept relatedness and concept-category relatedness base on the assumption that information carried in concept-concept links and concept-category links can mutually reinforce each other. Different from previous work, RCRank can not only find semantically related concepts but also interpret their relations by categories. Experimental results on concept recommendation and relation interpretation show that our method substantially outperforms classical methods.

Slinko and White, (2008) have recently introduced a new model of coalitional manipulation of voting rules under limited communication, which they call safe strategic voting. The computational aspects of this model were first studied by Hazon and Elkind, (2010), who provide polynomial-time algorithms for finding a safe strategic vote under k-approval and the Bucklin rule. In this paper, we answer an open question of Hazon and Elkind, (2010) by presenting a polynomial-time algorithm for finding a safe strategic vote under the Borda rule. Our results for Borda generalize to several interesting classes of scoring rules.

Scaling up the number of simultaneously moving units in pathfinding problems to hundreds, or even thousands, is well beyond the capability of theoretically optimal algorithms in practice, which is consistent with existing intractability results. Significant scalability can be achieved by trading off solution optimality, which motivates evaluating the quality of suboptimal solutions, especially in instances much larger than can be handled by optimal algorithms. We consider pathfinding in uniform cost grid maps, and we study the solution quality using the three most common quality criteria, total travel distance , sum of actions , and makespan . We focus on MAPP, which has been shown as state-of-the-art in terms of scalability and success ratio (i.e., percentage of solved units) on realistic game grid maps. Until now, the quality of MAPP's solutions had not been as extensively analyzed. We introduced enhancements that significantly improve MAPP's solution quality. For example, its sum of actions is cut to half on average. MAPP becomes competitive in terms of solution quality with FAR and WHCA*, two successful algorithms from the literature. To evaluate the quality of suboptimal solutions in instances beyond the capability of optimal algorithms, we use lower bounds of optimal values to show our solutions have a reasonable quality. For example, MAPP's average total travel distance is 19 percent longer than the lower bound.

When a system behaves abnormally, sequential diagnosis takes a sequence of measurements of the system until the faults causing the abnormality are identified, and the goal is to reduce the diagnostic cost, defined here as the number of measurements. To propose measurement points, previous work employs a heuristic based on reducing the entropy over a computed set of diagnoses. This approach generally has good performance in terms of diagnostic cost, but can fail to diagnose large systems when the set of diagnoses is too large. Focusing on a smaller set of probable diagnoses scales the approach but generally leads to increased average diagnostic costs. In this paper, we propose a new diagnostic framework employing four new techniques, which scales to much larger systems with good performance in terms of diagnostic cost. First, we propose a new heuristic for measurement point selection that can be computed efficiently, without requiring the set of diagnoses, once the system is modeled as a Bayesian network and compiled into a logical form known as d-DNNF. Second, we extend hierarchical diagnosis, a technique based on system abstraction from our previous work, to handle probabilities so that it can be applied to sequential diagnosis to allow larger systems to be diagnosed. Third, for the largest systems where even hierarchical diagnosis fails, we propose a novel method that converts the system into one that has a smaller abstraction and whose diagnoses form a superset of those of the original system; the new system can then be diagnosed and the result mapped back to the original system. Finally, we propose a novel cost estimation function which can be used to choose an abstraction of the system that is more likely to provide optimal average cost. Experiments with ISCAS-85 benchmark circuits indicate that our approach scales to all circuits in the suite except one that has a flat structure not susceptible to useful abstraction.

Set and multiset variables in constraint programming have typically been represented using subset bounds. However, this is a weak representation that neglects potentially useful information about a set such as its cardinality. For set variables, the length-lex (LL) representation successfully provides information about the length (cardinality) and position in the lexicographic ordering. For multiset variables, where elements can be repeated, we consider richer representations that take into account additional information. We study eight different representations in which we maintain bounds according to one of the eight different orderings: length-(co)lex (LL/LC), variety-(co)lex (VL/VC), length-variety-(co)lex (LVL/LVC), and variety-length-(co)lex (VLL/VLC) orderings. These representations integrate together information about the cardinality, variety (number of distinct elements in the multiset), and position in some total ordering. Theoretical and empirical comparisons of expressiveness and compactness of the eight representations suggest that length-variety-(co)lex (LVL/LVC) and variety-length-(co)lex (VLL/VLC) usually give tighter bounds after constraint propagation. We implement the eight representations and evaluate them against the subset bounds representation with cardinality and variety reasoning. Results demonstrate that they offer significantly better pruning and runtime.

We consider manipulation problems when the manipulator only has partial information about the votes of the nonmanipulators. Such partial information is described by an information set, which is the set of profiles of the nonmanipulators that are indistinguishable to the manipulator. Given such an information set, a dominating manipulation is a non-truthful vote that the manipulator can cast which makes the winner at least as preferable (and sometimes more preferable) as the winner when the manipulator votes truthfully. When the manipulator has full information, computing whether or not there exists a dominating manipulation is in P for many common voting rules (by known results). We show that when the manipulator has no information, there is no dominating manipulation for many common voting rules. When the manipulator's information is represented by partial orders and only a small portion of the preferences are unknown, computing a dominating manipulation is NP-hard for many common voting rules. Our results thus throw light on whether we can prevent strategic behavior by limiting information about the votes of other voters.

Nanson's and Baldwin's voting rules select a winner by successively eliminating candidates with low Borda scores. We show that these rules have a number of desirable computational properties. In particular, with unweighted votes, it is NP-hard to manipulate either rule with one manipulator, whilst with weighted votes, it is NP-hard to manipulate either rule with a small number of candidates and a coalition of manipulators. As only a couple of other voting rules are known to be NP-hard to manipulate with a single manipulator, Nanson's and Baldwin's rules appear to be particularly resistant to manipulation from a theoretical perspective. We also propose a number of approximation methods for manipulating these two rules. Experiments demonstrate that both rules are often difficult to manipulate in practice. These results suggest that elimination style voting rules deserve further study.

We propose an online form of the cake cutting problem. This models situations where agents arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the Dubins-Spanier moving knife procedure can be adapted to apply to such online problems. We propose some fairness properties that online cake cutting procedures can possess like online forms of proportionality and envy-freeness. We also consider the impact of collusion between agents. Finally, we study theoretically and empirically the competitive ratio of these online cake cutting procedures. Based on its resistance to collusion, and its good performance in practice, our results favour the online version of the cut-and-choose procedure over the online version of the moving knife procedure.

The ignoring delete lists relaxation is of paramount importance for both satisficing and optimal planning. In earlier work, it was observed that the optimal relaxation heuristic h+ has amazing qualities in many classical planning benchmarks, in particular pertaining to the complete absence of local minima. The proofs of this are hand-made, raising the question whether such proofs can be lead automatically by domain analysis techniques. In contrast to earlier disappointing results -- the analysis method has exponential runtime and succeeds only in two extremely simple benchmark domains -- we herein answer this question in the affirmative. We establish connections between causal graph structure and h+ topology. This results in low-order polynomial time analysis methods, implemented in a tool we call TorchLight. Of the 12 domains where the absence of local minima has been proved, TorchLight gives strong success guarantees in 8 domains. Empirically, its analysis exhibits strong performance in a further 2 of these domains, plus in 4 more domains where local minima may exist but are rare. In this way, TorchLight can distinguish ``easy'' domains from ``hard'' ones. By summarizing structural reasons for analysis failure, TorchLight also provides diagnostic output indicating domain aspects that may cause local minima.