Singleton Acyclic Mechanisms and their Applications to Scheduling Problems

Mehta, Roughgarden, and Sundararajan recently introduced a new class of cost sharing mechanisms called acyclic mechanisms}. These mechanisms achieve a slightly weaker notion of truthfulness than the well-known Moulin mechanisms, but provide additional freedom to improve budget balance and social cost approximation guarantees. In this paper, we investigate the potential of acyclic mechanisms for cost sharing games arising from combinatorial optimization problems. In particular, we study a subclass of acyclic mechanisms which we term singleton acyclic mechanisms}. We show that every} ρ-approximate algorithm for the underlying optimization problem can be turned into a singleton acyclic mechanism that is weakly-groupstrategyproof and ρ-budget balanced. Based on this result, we develop singleton acyclic mechanisms for parallel machine scheduling problems with completion time, flow time and makespan objectives. As it turns out, singleton acyclic mechanisms perform extremely well for completion time objectives both with respect to budget balance and social cost

Generalized Incremental Mechanisms for Scheduling Games

We study the problem of devising truthful mechanisms for cooperative cost sharing games that realize (approximate) budget balance and social cost. Recent negative results show that group-strategyproof mechanisms can only achieve very poor approximation guarantees for several fundamental cost sharing games. Driven by these limitations, we consider cost sharing mechanisms that realize the weaker notion of weak groupstrategyproofness. Mehta et al. [Games and Economic Behavior, 67:125–155, 2009] recently introduced the broad class of weakly group-strategyproof acyclic mechanisms and show that several primal-dual approximation algorithms naturally give rise to such mechanisms with attractive approximation guarantees. In this paper, we provide a simple yet powerful approach that enables us to turn any r-approximation algorithm into a r-budget balanced acyclic mechanism. We demonstrate the applicability of our approach by deriving weakly group-strategyproof mechanisms for several fundamental scheduling problems that outperform the best possible approximation guarantees of Moulin mechanisms. The mechanisms that we develop for completion time scheduling problems are the first mechanisms that achieve constant budget balance and social cost approximation factors. Interestingly, our mechanisms belong to the class of generalized incremental mechanisms proposed by Moulin [Social Choice and Welfare, 16:279–320, 1999]

Corporate agents

The logic of belief and intention in situations with multiple agents is increasingly well understood, but current formal approaches appear to face problems in applications where the number of agents greatly exceeds two. We provide an informal development of Corporate Agents, an intensional approximation of individual and group states which treats groups symmetrically with autonomous agents. Corporate Charters, constraints derived from typical patterns of information flow, replace detailed reasoning about the propagation of attitudes in most contexts. The approximation to an ideal logical formulation is not tight, but the model appears to function well in information-poor environments and fails in ways related to characteristic human errors. It may therefore be particularly appropriate to application in the area of natural language discourse

Conflict-driven learning in AI planning state-space search

Many combinatorial computation problems in computer science can be cast as a reachability problem in an implicitly described, potentially huge, graph: the state space. State-space search is a versatile and widespread method to solve such reachability problems, but it requires some form of guidance to prevent exploring that combinatorial space exhaustively. Conflict-driven learning is an indispensable search ingredient for solving constraint satisfaction problems (most prominently, Boolean satisfiability). It guides search towards solutions by identifying conflicts during the search, i.e., search branches not leading to any solution, learning from them knowledge to avoid similar conflicts in the remainder of the search. This thesis adapts the conflict-driven learning methodology to more general classes of reachability problems. Specifically, our work is placed in AI planning. We consider goal-reachability objectives in classical planning and in planning under uncertainty. The canonical form of "conflicts" in this context are dead-end states, i.e., states from which the desired goal property cannot be reached. We pioneer methods for learning sound and generalizable dead-end knowledge from conflicts encountered during forward state-space search. This embraces the following core contributions: When acting under uncertainty, the presence of dead-end states may make it impossible to satisfy the goal property with absolute certainty. The natural planning objective then is MaxProb, maximizing the probability of reaching the goal. However, algorithms for MaxProb probabilistic planning are severely underexplored. We close this gap by developing a large design space of probabilistic state-space search methods, contributing new search algorithms, admissible state-space reduction techniques, and goal-probability bounds suitable for heuristic state-space search. We systematically explore this design space through an extensive empirical evaluation. The key to our conflict-driven learning algorithm adaptation are unsolvability detectors, i.e., goal-reachability overapproximations. We design three complementary families of such unsolvability detectors, building upon known techniques: critical-path heuristics, linear-programming-based heuristics, and dead-end traps. We develop search methods to identify conflicts in deterministic and probabilistic state spaces, and we develop suitable refinement methods for the different unsolvability detectors so to recognize these states. Arranged in a depth-first search, our techniques approach the elegance of conflict-driven learning in constraint satisfaction, featuring the ability to learn to refute search subtrees, and intelligent backjumping to the root cause of a conflict. We provide a comprehensive experimental evaluation, demonstrating that the proposed techniques yield state-of-the-art performance for finding plans for solvable classical planning tasks, proving classical planning tasks unsolvable, and solving MaxProb in probabilistic planning, on benchmarks where dead-end states abound.Viele kombinatorisch komplexe Berechnungsprobleme in der Informatik lassen sich als Erreichbarkeitsprobleme in einem implizit dargestellten, potenziell riesigen, Graphen - dem Zustandsraum - verstehen. Die Zustandsraumsuche ist eine weit verbreitete Methode, um solche Erreichbarkeitsprobleme zu lösen. Die Effizienz dieser Methode hängt aber maßgeblich von der Verwendung strikter Suchkontrollmechanismen ab. Das konfliktgesteuerte Lernen ist eine essenzielle Suchkomponente für das Lösen von Constraint-Satisfaction-Problemen (wie dem Erfüllbarkeitsproblem der Aussagenlogik), welches von Konflikten, also Fehlern in der Suche, neue Kontrollregeln lernt, die ähnliche Konflikte zukünftig vermeiden. In dieser Arbeit erweitern wir die zugrundeliegende Methodik auf Zielerreichbarkeitsfragen, wie sie im klassischen und probabilistischen Planen, einem Teilbereich der Künstlichen Intelligenz, auftauchen. Die kanonische Form von „Konflikten“ in diesem Kontext sind sog. Sackgassen, Zustände, von denen aus die Zielbedingung nicht erreicht werden kann. Wir präsentieren Methoden, die es ermöglichen, während der Zustandsraumsuche von solchen Konflikten korrektes und verallgemeinerbares Wissen über Sackgassen zu erlernen. Unsere Arbeit umfasst folgende Beiträge: Wenn der Effekt des Handelns mit Unsicherheiten behaftet ist, dann kann die Existenz von Sackgassen dazu führen, dass die Zielbedingung nicht unter allen Umständen erfüllt werden kann. Die naheliegendste Planungsbedingung in diesem Fall ist MaxProb, das Maximieren der Wahrscheinlichkeit, dass die Zielbedingung erreicht wird. Planungsalgorithmen für MaxProb sind jedoch wenig erforscht. Um diese Lücke zu schließen, erstellen wir einen umfangreichen Bausatz für Suchmethoden in probabilistischen Zustandsräumen, und entwickeln dabei neue Suchalgorithmen, Zustandsraumreduktionsmethoden, und Abschätzungen der Zielerreichbarkeitswahrscheinlichkeit, wie sie für heuristische Suchalgorithmen gebraucht werden. Wir explorieren den resultierenden Gestaltungsraum systematisch in einer breit angelegten empirischen Studie. Die Grundlage unserer Adaption des konfliktgesteuerten Lernens bilden Unerreichbarkeitsdetektoren. Wir konzipieren drei Familien solcher Detektoren basierend auf bereits bekannten Techniken: Kritische-Pfad Heuristiken, Heuristiken basierend auf linearer Optimierung, und Sackgassen-Fallen. Wir entwickeln Suchmethoden, um Konflikte in deterministischen und probabilistischen Zustandsräumen zu erkennen, sowie Methoden, um die verschiedenen Unerreichbarkeitsdetektoren basierend auf den erkannten Konflikten zu verfeinern. Instanziiert als Tiefensuche weisen unsere Techniken ähnliche Eigenschaften auf wie das konfliktgesteuerte Lernen für Constraint-Satisfaction-Problemen. Wir evaluieren die entwickelten Methoden empirisch, und zeigen dabei, dass das konfliktgesteuerte Lernen unter gewissen Voraussetzungen zu signifikanten Suchreduktionen beim Finden von Plänen in lösbaren klassischen Planungsproblemen, Beweisen der Unlösbarkeit von klassischen Planungsproblemen, und Lösen von MaxProb im probabilistischen Planen, führen kann

Approximation Algorithms for Resource Allocation

This thesis is devoted to designing new techniques and algorithms for combinatorial optimization problems arising in various applications of resource allocation. Resource allocation refers to a class of problems where scarce resources must be distributed among competing agents maintaining certain optimization criteria. Examples include scheduling jobs on one/multiple machines maintaining system performance; assigning advertisements to bidders, or items to people maximizing profit/social fairness; allocating servers or channels satisfying networking requirements etc. Altogether they comprise a wide variety of combinatorial optimization problems. However, a majority of these problems are NP-hard in nature and therefore, the goal herein is to develop approximation algorithms that approximate the optimal solution as best as possible in polynomial time. The thesis addresses two main directions. First, we develop several new techniques, predominantly, a new linear programming rounding methodology and a constructive aspect of a well-known probabilistic method, the Lov\'{a}sz Local Lemma (LLL). Second, we employ these techniques to applications of resource allocation obtaining substantial improvements over known results. Our research also spurs new direction of study; we introduce new models for achieving energy efficiency in scheduling and a novel framework for assigning advertisements in cellular networks. Both of these lead to a variety of interesting questions. Our linear programming rounding methodology is a significant generalization of two major rounding approaches in the theory of approximation algorithms, namely the dependent rounding and the iterative relaxation procedure. Our constructive version of LLL leads to first algorithmic results for many combinatorial problems. In addition, it settles a major open question of obtaining a constant factor approximation algorithm for the Santa Claus problem. The Santa Claus problem is a $NP$-hard resource allocation problem that received much attention in the last several years. Through out this thesis, we study a number of applications related to scheduling jobs on unrelated parallel machines, such as provisionally shutting down machines to save energy, selectively dropping outliers to improve system performance, handling machines with hard capacity bounds on the number of jobs they can process etc. Hard capacity constraints arise naturally in many other applications and often render a hitherto simple combinatorial optimization problem difficult. In this thesis, we encounter many such instances of hard capacity constraints, namely in budgeted allocation of advertisements for cellular networks, overlay network design, and in classical problems like vertex cover, set cover and k-median