293 research outputs found

    ‘Strong’–‘weak’ precedence in scheduling: Extensions to series–parallel orders

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    AbstractWe examine computational complexity implications for scheduling problems with job precedence relations with respect to strong precedence versus weak precedence. We propose a consistent definition of strong precedence for chains, trees, and series–parallel orders. Using modular decomposition for partially ordered sets (posets), we restate and extend past complexity results for chains and trees as summarized in Dror (1997) [5]. Moreover, for series–parallel posets we establish new computational complexity results for strong precedence constraints for single- and multi-machine problems

    Sequential Relational Decomposition

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    The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple and natural formalization of sequential decomposition, in which a task is decomposed into two sequential sub-tasks, with the first sub-task to be executed before the second sub-task is executed. These tasks are specified by means of input/output relations. We define and study decomposition problems, which is to decide whether a given specification can be sequentially decomposed. Our main result is that decomposition itself is a difficult computational problem. More specifically, we study decomposition problems in three settings: where the input task is specified explicitly, by means of Boolean circuits, and by means of automatic relations. We show that in the first setting decomposition is NP-complete, in the second setting it is NEXPTIME-complete, and in the third setting there is evidence to suggest that it is undecidable. Our results indicate that the intuitive idea of decomposition as a system-design approach requires further investigation. In particular, we show that adding a human to the loop by asking for a decomposition hint lowers the complexity of decomposition problems considerably

    The power of foregone payoffs: a mousetracking study

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    Behavior in two-player laboratory games has been observed to depend upon choices that the other player "could have made," in violation of the principle of subgame perfection. Models of other-regarding preferences that only transform payoffs at end-nodes (e.g. inequality aversion) cannot explain this behavior, and various explanations (e.g. models of intention-based reciprocity) have been proposed. We explore the mechanisms by which foregone payoffs influence decision-making in a variety of two-player, two-stage games using mousetracking, a technology that allows us to observe which payoffs subjects attend to, and for how long, when making strategic decisions

    Aggregate Matchings

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    This paper characterizes the testable implications of stability for aggregate matchings. We consider data on matchings where individuals are aggregated, based on their observable characteristics, into types, and we know how many agents of each type match. We derive stability conditions for an aggregate matching, and, based on these, provide a simple necessary and sufficient condition for an observed aggregate matching to be rationalizable (i.e. such that preferences can be found so that the observed aggregate matching is stable). Subsequently, we derive moment inequalities based on the stability conditions, and provide an empirical illustration using the cross-sectional marriage distributions across the US states
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