Modern society is critically dependent on the services provided by engineered infrastructure networks. When natural disasters (e.g. Hurricane Sandy) occur, the ability of these networks to provide service is often degraded because of physical damage to network components. One of the most critical of these networks is the electrical distribution grid, with medium voltage circuits often suffering the most severe damage. However, well-placed upgrades to these distribution grids can greatly improve post-event network performance. We formulate an optimal electrical distribution grid design problem as a two-stage, stochastic mixed-integer program with damage scenarios from natural disasters modeled as a set of stochastic events. We develop and investigate the tractability of an exact and several heuristic algorithms based on decompositions that are hybrids of techniques developed by the AI and operations research communities. We provide computational evidence that these algorithms have significant benefits when compared with commercial, mixed-integer programming software.

Data-driven analytics — in areas ranging from consumer marketing to public policy — often allow behavior prediction at the level of individuals rather than population segments , offering the opportunity to improve decisions that impact large populations. Modeling such (generalized) assignment problems as linear programs, we propose a general value-directed compression technique for solving such problems at scale. We dynamically segment the population into cells using a form of column generation, constructing groups of individuals who can provably be treated identically in the optimal solution. This compression allows problems, unsolvable using standard LP techniques, to be solved effectively. Indeed, once a compressed LP is constructed, problems can solved in milliseconds. We provide a theoretical analysis of themethods, outline the distributed implementation of the requisite data processing, and show how a single compressed LP can be used to solve multiple variants of the original LP near-optimally in real-time (e.g., tosupport scenario analysis). We also show how the method can be leveraged in integer programming models.  Experimental results on marketing contact optimization and political legislature problems validate the performance of our technique.

In this paper we show that the alpha-beta algorithm and its successor MT-SSS*, as two classic minimax search algorithms, can be implemented as rollout algorithms , a generic algorithmic paradigm widely used in many domains. Specifically, we define a family of rollout algorithms, in which the rollout policy is restricted to select successor nodes only from a certain subset of the children list. We show that any rollout policy in this family (either deterministic or randomized) is guaranteed to evaluate the game tree correctly with a finite number of rollouts. Moreover, we identify simple rollout policies in this family that ``implement'' alpha-beta and MT-SSS*. Specifically, given any game tree, the rollout algorithms with these particular policies always visit the same set of leaf nodes in the same order with alpha-beta and MT-SSS*, respectively. Our results suggest that traditional pruning techniques and the recent Monte Carlo Tree Search algorithms, as two competing approaches for game tree evaluation, may be unified under the rollout paradigm.

In this paper, we formulate a new problem related to the well-known influence maximization in the context of computational advertising. Our new problem considers allocating marketing channels (e.g., TV, newspaper, and websites) to advertisers from the view point of a match maker, which was not taken into account in previous studies on the influence maximization. The objective of the problem is to find an allocation such that each advertiser can influence some given number of customers while the slots of marketing channels are limited. We propose an algorithm based on the Lagrangian decomposition. We empirically show that our algorithm computes better quality solutions than existing algorithms, scales up to graphs of 10M vertices, and performs well particularly in a parallel environment.

Satisfiability Modulo Theories (SMT) is essential for many practical applications, e.g., in hard- and software verification, and increasingly also in other scientific areas like computational biology. A large number of applications in these areas benefit from bit-precise reasoning over finite-domain variables. Current approaches in this area translate a formula over bit-vectors to an equisatisfiable propositional formula, which is then given to a SAT solver. In this paper, we present a novel stochastic local search (SLS) algorithm to solve SMT problems, especially those in the theory of bit-vectors, directly on the theory level. We explain how several successful techniques used in modern SLS solvers for SAT can be lifted to the SMT level. Experimental results show that our approach can compete with state-of-the-art bit-vector solvers on many practical instances and, sometimes, outperform existing solvers. This offers interesting possibilities in combining our approach with existing techniques, and, moreover, new insights into the importance of exploiting problem structure in SLS solvers for SAT. Our approach is modular and, therefore, extensible to support other theories, potentially allowing SLS to become part of the more general SMT framework.

The problem of computing optimal strategy to commit to in various games has attracted intense research interests and has important real-world applications such as security (attacker-defender) games. In this paper, we consider the problem of computing optimal leader’s machine to commit to in two-person repeated game, where the follower also plays a machine strategy. Machine strategy is the generalized notion of automaton strategy, where the number of states in the automaton can be possibly infinite. We begin with the simple case where both players are confined to automata strategies, and then extend to general (possibly randomized) machine strategies. We first give a concise linear program to compute the optimal leader’s strategy and give two efficient implementations of the linear program: one via enumeration of a convex hull and the other via randomization. We then investigate the case where two machines have different levels of intelligence in the sense that one machine is able to record more history information than the other. We show that an intellectually superior leader, sometimes considered being exploited by the follower, can figure out the follower’s machine by brute-force and exploit the follower in return.

In designing an exchange mechanism, it is important to Exchange markets (aka double auctions) are the most important achieve a number of desirable properties, namely: maximizing institutions for modern economy, which are centralized social welfare (i.e., efficient), preventing manipulations markets consisting of exchange rules for traders to buy and of agents (i.e., truthful), an agent never pays more sell commodities, e.g. stock exchanges. Most existing studies than what she gets (i.e., individually rational) and the market of exchanges are for the environments where a trader maker should not run the mechanism with a deficit (i.e., is either a buyer or a seller, but not both, of certain commodities budget balanced). It is well known that designing an exchange (Myerson and Satterthwaite 1983; McAfee 1992; mechanism that is efficient, truthful, individually rational Wurman, Walsh, and Wellman 1998; Blum, Sandholm, and and budget balanced is impossible (Myerson and Satterthwaite Zinkevich 2006; Bredin, Parkes, and Duong 2007; Parsons, 1983). Since a loss-making mechanism does not Rodriguez-Aguilar, and Klein 2011).

Increased interest in web-based education has spurred the proliferation of online learning environments. However, these platforms suffer from high dropout rates due to lack of sustained motivation among the students taking the course. In an effort to address this problem, we propose an incentive-based, instructor-driven approach to orchestrate the interactions in online educational forums (OEFs). Our approach takes into account the heterogeneity in skills among the students as well as the limited budget available to the instructor. We first analytically model OEFs in a non-strategic setting using ideas from lumpable continuous time Markov chains and compute expected aggregate transient net-rewards for the instructor and the students. We next consider a strategic setting where we use the rewards computed above to set up a mixed-integer linear program which views an OEF as a single-leader-multiple-followers Stackelberg game and recommends an optimal plan to the instructor for maximizing student participation. Our experimental results reveal several interesting phenomena including a striking non-monotonicity in the level of participation of students vis-a-vis the instructor's arrival rate.

We consider the problem of fair division of a two dimensional heterogeneous good among several agents. Applications include division of land as well as ad space in print and electronic media. Classical cake cutting protocols either consider a one-dimensional resource, or allocate each agent several disconnected pieces. In practice, however, the two dimensional shape of the allotted piece is of crucial importance in many applications, e.g., squares or bounded aspect-ratio rectangles are most useful for building houses as well as advertisements. We thus introduce and study the problem of envy-free two-dimensional division wherein the utility of the agents depends on the geometric shape of the allocated pieces (as well as the location and size). In addition to envy-freeness, we require that the fraction allocated to each agent be at least a certain constant that depends only on the shape of the cake and the number of agents. We focus on the case where the allotted pieces must be square and the cakes are either squares or the unbounded plane. We provide algorithms for the problem for settings with two and three agents.

Following recent studies of iterative voting and its effects on plurality vote outcomes, we provide characterisations and complexity results for three models of iterative voting under the plurality rule. Our focus is on providing a better understanding regarding the set of equilibria attainable by iterative voting processes. We start with the basic model of plurality voting. We first establish some useful properties of equilibria, reachable by iterative voting, which enable us to show that deciding whether a given profile is an iteratively reachable equilibrium is NP-complete. We then proceed to combine iterative voting with the concept of truth bias, a model where voters prefer to be truthful when they cannot affect the outcome. We fully characterise the set of attainable truth-biased equilibria, and show that it is possible to determine all such equilibria in polynomial time. Finally, we also examine the model of lazy voters, in which a voter may choose to abstain from the election. We establish convergence of the iterative process, albeit not necessarily to a Nash equilibrium. As in the case with truth bias, we also provide a polynomial time algorithm to find all the attainable equilibria.