19,852 research outputs found
Formal Derivation of Concurrent Garbage Collectors
Concurrent garbage collectors are notoriously difficult to implement
correctly. Previous approaches to the issue of producing correct collectors
have mainly been based on posit-and-prove verification or on the application of
domain-specific templates and transformations. We show how to derive the upper
reaches of a family of concurrent garbage collectors by refinement from a
formal specification, emphasizing the application of domain-independent design
theories and transformations. A key contribution is an extension to the
classical lattice-theoretic fixpoint theorems to account for the dynamics of
concurrent mutation and collection.Comment: 38 pages, 21 figures. The short version of this paper appeared in the
Proceedings of MPC 201
Ambiguities in order-theoretic formulations of thermodynamics
Since the 1909 work of Carath\'eodory, formulations of thermodynamics have
gained ground which highlight the role of the the binary relation of adiabatic
accessibility between equilibrium states. A feature of Carath\'eodory's system
is that the version therein of the second law contains an ambiguity about the
nature of irreversible adiabatic processes, making it weaker than the
traditional Kelvin-Planck statement of the law. This paper attempts first to
clarify the nature of this ambiguity, by defining the arrow of time in
thermodynamics by way of the Equilibrium Principle ("Minus First Law"). It then
argues that the ambiguity reappears in the important 1999 axiomatisation due to
Lieb and Yngvason.Comment: 13 pages, 1 figur
Reversible simulation of bipartite product Hamiltonians
Consider two quantum systems A and B interacting according to a product
Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used
to simulate each other reversibly (i.e., without efficiency losses) with the
help of local unitary operations and local ancillas. Accordingly, all non-local
features of a product Hamiltonian -- including the rate at which it can be used
to produce entanglement, transmit classical or quantum information, or simulate
other Hamiltonians -- depend only upon a single parameter. We identify this
parameter and use it to obtain an explicit expression for the entanglement
capacity of all product Hamiltonians. Finally, we show how the notion of
simulation leads to a natural formulation of measures of the strength of a
nonlocal Hamiltonian.Comment: 10 page
Workload Equity in Vehicle Routing Problems: A Survey and Analysis
Over the past two decades, equity aspects have been considered in a growing
number of models and methods for vehicle routing problems (VRPs). Equity
concerns most often relate to fairly allocating workloads and to balancing the
utilization of resources, and many practical applications have been reported in
the literature. However, there has been only limited discussion about how
workload equity should be modeled in VRPs, and various measures for optimizing
such objectives have been proposed and implemented without a critical
evaluation of their respective merits and consequences.
This article addresses this gap with an analysis of classical and alternative
equity functions for biobjective VRP models. In our survey, we review and
categorize the existing literature on equitable VRPs. In the analysis, we
identify a set of axiomatic properties that an ideal equity measure should
satisfy, collect six common measures, and point out important connections
between their properties and those of the resulting Pareto-optimal solutions.
To gauge the extent of these implications, we also conduct a numerical study on
small biobjective VRP instances solvable to optimality. Our study reveals two
undesirable consequences when optimizing equity with nonmonotonic functions:
Pareto-optimal solutions can consist of non-TSP-optimal tours, and even if all
tours are TSP optimal, Pareto-optimal solutions can be workload inconsistent,
i.e. composed of tours whose workloads are all equal to or longer than those of
other Pareto-optimal solutions. We show that the extent of these phenomena
should not be underestimated. The results of our biobjective analysis are valid
also for weighted sum, constraint-based, or single-objective models. Based on
this analysis, we conclude that monotonic equity functions are more appropriate
for certain types of VRP models, and suggest promising avenues for further
research.Comment: Accepted Manuscrip
Compensations in the Shapley value and the compensation solutions for graph games
We consider an alternative expression of the Shapley value that reveals a system of compensations: each player receives an equal share of the worth of each coalition he belongs to, and has to compensate an equal share of the worth of any coalition he does not belong to. We give an interpretation in terms of formation of the grand coalition according to an ordering of the players and define the corresponding compensation vector. Then, we generalize this idea to cooperative games with a communication graph. Firstly, we consider cooperative games with a forest (cycle-free graph). We extend the compensation vector by considering all rooted spanning trees of the forest (see Demange 2004) instead of orderings of the players. The associated allocation rule, called the compensation solution, is characterized by component efficiency and relative fairness. The latter axiom takes into account the relative position of a player with respect to his component. Secondly, we consider cooperative games with arbitrary graphs and construct rooted spanning trees by using the classical algorithms DFS and BFS. If the graph is complete, we show that the compensation solutions associated with DFS and BFS coincide with the Shapley value and the equal surplus division respectively.
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