Integer Linear Programming (ILP) and its mixed variant (MILP) are archetypical examples of NP-complete optimization problems which have a wide range of applications in various areas of artificial intelligence. However, we still lack a thorough understanding of which structural restrictions make these problems tractable. Here we focus on structure captured via so-called decompositional parameters, which have been highly successful in fields such as boolean satisfiability and constraint satisfaction but have not yet reached their full potential in the ILP setting. In particular, primal treewidth (an established decompositional parameter) can only be algorithmically exploited to solve ILP under restricted circumstances. Our main contribution is the introduction and algorithmic exploitation of two new decompositional parameters for ILP and MILP. The first, torso-width, is specifically tailored to the linear programming setting and is the first decompositional parameter which can also be used for MILP. The latter, incidence treewidth, is a concept which originates from boolean satisfiability but has not yet been used in the ILP setting; here we obtain a full complexity landscape mapping the precise conditions under which incidence treewidth can be used to obtain efficient algorithms. Both of these parameters overcome previous shortcomings of primal treewidth for ILP in unique ways, and consequently push the frontiers of tractability for these important problems.

A grid maze is a binary matrix where fields containing a 0 are accessible while fields containing a 1 are blocked. A movement sequence consists of relative movements up, down, left, right – moving to a blocked field results in non-movement. The simultaneous maze solving problem asks for the shortest movement sequence starting in the upper left corner and visiting the lower right corner for all mazes of size n × m (for which a path from the upper left to the lower right corner exists at all). We present a theoretical problem analysis, including hardness results and a cubic upper bound on the sequence length. In addition, we describe several approaches to practically compute solving sequences and lower bounds despite the high combinatorial complexity of the problem.

In the recent years, there has been significant work on the difficulty of heuristic search problems, identifying different problem instance characteristics that can have a significant impact on search effort. Phase transitions in the solubility of random problem instances have proved useful in the study of problem difficulty for other classes of computational problems, notably SAT and CSP, and it has been shown that the hardest problems typically occur during this rapid transition. In this work, we perform the first empirical investigation of the phase transition phenomena for heuristic search. We establish the existence of a rapid transition in the solubility of an abstract model of heuristic search problems and show that, for greedy best first search, the hardest instances are associated with the phase transition region. We then perform a novel investigation of the behavior of heuristics of different strength across the solubility spectrum. Finally, we demonstrate that the behavior of our abstract model carries over to commonly used benchmark problems including the Pancake Problem, Grid Navigation, TopSpin, and the Towers of Hanoi. An interesting deviation is observed and explained in the Sliding Puzzle.

Metaheuristics have been developed to provide general purpose approaches for solving hard combinatorial problems. While these frameworks often serve as the starting point for the development of problem-specific search procedures, they very rarely work efficiently in their default state. We combine the ideas of reactive search, which adjusts key parameters during search, and algorithm configuration, which fine-tunes algorithm parameters for a given set of problem instances, for the automatic compilation of a portfolio of highly reactive dialectic search heuristics for MaxSAT. Even though the dialectic search metaheuristic knows nothing more about MaxSAT than how to evaluate the cost of a truth assignment, our automatically generated solver defines a new state of the art for random weighted partial MaxSAT instances. Moreover, when combined with an industrial MaxSAT solver, the self-assembled reactive portfolio was able to win four out of nine gold medals at the recent 2016 MaxSAT Evaluation on random, crafted, and industrial partial and weighted-partial MaxSAT instances.

Selling reserved instances (or virtual machines) is a basic service in cloud computing. In this paper, we consider a more flexible pricing model for instance reservation, in which a customer can propose the time length and number of resources of her request, while in today's industry, customers can only choose from several predefined reservation packages. Under this model, we design randomized mechanisms for customers coming online to optimize social welfare and providers' revenue. We first consider a simple case, where the requests from the customers do not vary too much in terms of both length and value density. We design a randomized mechanism that achieves a competitive ratio 1/42 for both social welfare and revenue, which is a improvement as there is usually no revenue guarantee in previous works such as (Azar et al. 2015; Wang et al. 2015. This ratio can be improved up to 1/11 when we impose a realistic constraint on the maximum number of resources used by each request. On the hardness side, we show an upper bound 1/3 on competitive ratio for any randomized mechanism.We then extend our mechanism to the general case and achieve a competitive ratio 1/42⌈log k ⌉ log T for both social welfare and revenue, where T is the ratio of the maximum request length to the minimum request length and k is the ratio of the maximum request value density to the minimum request value density. This result outperforms the previous upper bound 1/ CkT for deterministic mechanisms (Wang et al. 2015). We also prove an upper bound 2/log 8 kT for any randomized mechanism. All the mechanisms we provide are in a greedy style. They are truthful and easy to be integrated into practical cloud systems.

Proper scoring rules can be used to incentivize a forecaster to truthfully report her private beliefs about the probabilities of future events and to evaluate the relative accuracy of forecasters. While standard scoring rules can score forecasts only once the associated events have been resolved, many applications would benefit from instant access to proper scores. In forecast aggregation, for example, it is known that using weighted averages, where more weight is put on more accurate forecasters, outperforms simple averaging of forecasts. We introduce proxy scoring rules, which generalize proper scoring rules and, given access to an appropriate proxy, allow for immediate scoring of probabilistic forecasts. In particular, we suggest a proxy-scoring generalization of the popular quadratic scoring rule, and characterize its incentive and accuracy evaluation properties theoretically. Moreover, we thoroughly evaluate it experimentally using data from a large real world geopolitical forecasting tournament, and show that it is competitive with proper scoring rules when the number of questions is small.

The dollar auction is an auction model used to analyse the dynamics of conflict escalation. In this paper, we analyse the course of an auction when participating players are spiteful, i.e., they are motivated not only by their own profit, but also by the desire to hurt the opponent. We investigate this model for the complete information setting, both for the standard scenario and for the situation where auction starts with non-zero bids. Our results give us insight into the possible effects of meanness onto conflict escalation.

In this paper, we analyze an emerging economic form, called fans economy, in which a fan donates money to the host and gets allocated proportional to the amount of his donation (normalized by the overall amount of donation). Fans economy is the major way live streaming apps monetize and includes a number of popular economic forms ranging from crowdfunding to mutual fund. We propose an auction game, coined all-pay auctions with proportional allocation (APAPA), to model the fans economy and analyze the auction from the perspective of revenue. Comparing to the standard all-pay auction, which normally has no pure Nash-Equilibrium in the complete information setting, we solve the pure Nash-Equilibrium of the APAPA in closed form and prove its uniqueness. Motivated by practical concerns, we then analyze the case where APAPA is equipped with a reserve and show that there might be multiple equilibria in this case. We give an efficient algorithm to compute all equilibria in this case. For either case, with or without reserve, we show that APAPA always extracts revenue that 2-approximates the second-highest valuation. Furthermore, we conduct experiments to show how revenue changes with respect to different reserves.

We consider voting under metric preferences: both voters and candidates are associated with points in a metric space, and each voter prefers candidates that are closer to her to ones that are further away. In this setting, it is often desirable to select a candidate that minimizes the sum of distances to the voters. However, common voting rules operate on voters' preference rankings and therefore may be unable to identify the best candidate. A relevant measure of the quality of a voting rule is then its distortion, defined as the worst-case ratio between the performance of a candidate selected by the rule and that of an optimal candidate. Anshelevich, Bhardwaj and Postl show that some popular rules such as Borda and Plurality do badly in this regard: their distortion scales linearly with the number of candidates. On the positive side, Anshelevich et al. identify a few voting rules whose distortion is bounded by a constant; however, these rules are rarely used in practice. In this paper, we analyze the distortion of two widely used (classes of) voting rules, namely, scoring rules and Single Transferable Vote (STV). We show that all scoring rules have super-constant distortion, answering a question that was left open by Anshelevich et al.; however, we identify a scoring rule whose distortion is asymptotically better than that of Plurality and Borda. For STV, we obtain an upper bound of O (log m ), where m is the number of candidates, as well as a super-constant lower bound; thus, STV is a reasonable, though not a perfect rule from this perspective.

One of the fundamental research challenges in network science is the centrality analysis, i.e., identifying the nodes that play the most important roles in the network. In this paper, we focus on the game-theoretic approach to centrality analysis. While various centrality indices have been proposed based on this approach, it is still unknown what distinguishes this family of indices from the more classical ones. In this paper, we answer this question by providing the first axiomatic characterization of game-theoretic centralities. Specifically, we show that every centrality can be obtained following the game-theoretic approach, and show that two natural classes of game-theoretic centrality can be characterized by two intuitive properties pertaining to Myerson's notion of Fairness.