37,847 research outputs found

    Discounted Tree Solutions

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    This article introduces a discount parameter and a weight function in Myerson's (1977) classical model of cooperative games with restrictions on cooperation. The discount parameter aims to reflect the time preference of the agents while the weight function aims to reflect the importance of each node of a graph. We provide axiomatic characterizations of two types of solution that are inspired by the hierarchical outcomes (Demange, 2004)

    Optimal Approximation Algorithms for Multi-agent Combinatorial Problems with Discounted Price Functions

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    Submodular functions are an important class of functions in combinatorial optimization which satisfy the natural properties of decreasing marginal costs. The study of these functions has led to strong structural properties with applications in many areas. Recently, there has been significant interest in extending the theory of algorithms for optimizing combinatorial problems (such as network design problem of spanning tree) over submodular functions. Unfortunately, the lower bounds under the general class of submodular functions are known to be very high for many of the classical problems. In this paper, we introduce and study an important subclass of submodular functions, which we call discounted price functions. These functions are succinctly representable and generalize linear cost functions. In this paper we study the following fundamental combinatorial optimization problems: Edge Cover, Spanning Tree, Perfect Matching and Shortest Path, and obtain tight upper and lower bounds for these problems. The main technical contribution of this paper is designing novel adaptive greedy algorithms for the above problems. These algorithms greedily build the solution whist rectifying mistakes made in the previous steps

    Expectation Optimization with Probabilistic Guarantees in POMDPs with Discounted-sum Objectives

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    Partially-observable Markov decision processes (POMDPs) with discounted-sum payoff are a standard framework to model a wide range of problems related to decision making under uncertainty. Traditionally, the goal has been to obtain policies that optimize the expectation of the discounted-sum payoff. A key drawback of the expectation measure is that even low probability events with extreme payoff can significantly affect the expectation, and thus the obtained policies are not necessarily risk-averse. An alternate approach is to optimize the probability that the payoff is above a certain threshold, which allows obtaining risk-averse policies, but ignores optimization of the expectation. We consider the expectation optimization with probabilistic guarantee (EOPG) problem, where the goal is to optimize the expectation ensuring that the payoff is above a given threshold with at least a specified probability. We present several results on the EOPG problem, including the first algorithm to solve it.Comment: Full version of a paper published at IJCAI/ECAI 201

    A survey of max-type recursive distributional equations

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    In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X =^d g((\xi_i,X_i),i\geq 1). Here (\xi_i) and g(\cdot) are given and the X_i are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g(\cdot) is essentially a ``maximum'' or ``minimum'' function. We draw attention to the theoretical question of endogeny: in the associated recursive tree process X_i, are the X_i measurable functions of the innovations process (\xi_i)?Comment: Published at http://dx.doi.org/10.1214/105051605000000142 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

    Managing Forests for Multiple Tradeoffs: Compromising on Timber, Carbon, and Biodiversity Objectives

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    In this paper, we develop a multiple objective, decision-making model that focuses on forest policies that simultaneously achieve carbon uptake and maintenance of ecosystem diversity objectives. Two forest carbon measures are used – a nominal (undiscounted) net carbon uptake as a proxy for long-term carbon sequestration and discounted net carbon uptake that captures the “fast” carbon accumulation aspect. Ecosystem diversity is expressed in terms of desired structures for forest and afforested agricultural land. Economic effects of possible strategies are examined by comparing attainment of these objectives with the net discounted returns from commercial timber harvests and agricultural activities. The tradeoffs between timber and non-timber objectives are obtained by means of compromise programming. Two measures of distance between the current objective values and the ideal ones are used to assess attainment of multiple goals. We explore how the choice of a measure affects the decisions and overall performance. The model is applied to the boreal forest and accompanying marginal agricultural lands in the Peace River region of northeastern British Columbia.biological and ecosystem diversity, compromise programming, forest carbon sequestration, forest management, multiple objectives

    PHYLOGENY OF SOME MIDDLE AMERICAN PITVIPERS BASED ON A CLADISTIC ANALYSIS OF MITOCHONDRIAL 12S AND 16S DNA SEQUENCE INFORMATION

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    The cladistic relationships of several Middle American pitvipers representing the genera Bothrops (sensu stricto), Bothriechis, Cerrophidion, Lachesis and Porthidium were determined using mitochondrial 12S and 16S DNA sequence information. Maximum parsimony analyses were performed using PAUP on aligned sequences that included published information for related taxa. Two sets of analyses were conducted: one disregarding gaps in the aligned matrix, and another with gaps treated as a fifth base. When gaps were excluded resolution declined, although the general arrangement of the taxa changed little. A consistent relationship was the grouping of ((Porthidium, Bothriechis) Lachesis). The placement of Lachesis, as nested within other bothropoid genera, is only partially supported by results of other authors. The arrangement of Crotalus, Bothrops and Cerrophidion was ambiguous when gaps were discounted. In both trees, Agkistrodon was basal to the New World forms. The remaining genera, Trimeresurus (Protobothrops), Vipera, Azemiops, and Coluber, were uniformly distant to the former taxa. Also of interest is the lack of close relationship, based on the DNA data here and elsewhere, between Bothrops and Porthidium. This is in striking contrast to results based on morphologic and allozymic analyses of previous studies. It is concluded that additional DNA sequence information from a larger sample of taxa will be necessary to better assess the phylogenetic relationships among Middle American and related pitvipers
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