39763724
Branch and bound on the network model
Abstract Karp and Zhang developed a general randomized parallel algorithm for solving branch and bound problems. They showed that with high probability their algorithm attained optimal speedup within a constant factor (for p⩽ n/( log n) c , where p is the number of processors, n is the “size” of the problem, and c is a constant). Ranade later simplified the analysis and obtained a better processor bound. Karp and Zhang's algorithm works on models of computation where communication cost is constant. The present paper considers the Branch and Bound problem on networks where the communication cost is high. Suppose sending a message in a p processor network takes G = O ( log p) time and node expansion (defined below) takes unit time (other operations being free). Then a simple randomized algorithm is presented which is, asymptotically, nearly optimal for p = O (2 log c n ) , where c is any constant and n is the number of nodes in the input tree with cost no greater than the cost of the optimal leaf in the tree.
1576847
On Aggregating Teams of Learning Machines
The present paper studies the problem of when a team of learning machines can be aggregated into a single learning machine without any loss in learning power. The main results concern aggregation ratios for vacillatory identification of languages from texts. For a positive integer n, a machine is said to TxtFexn-identify a language L just in case the machine converges to upto n grammars for L on any text for L. For such identification criteria, the aggregation ratio is derived for the n=2 case. It is shown that the collection of languages that can be TxtFex2 identified by teams with success ratio greater than 5/6 are the same as those collections of languages that can be TxtFex2-identified by a single machine. It is also established that 5/6 is indeed the cut-off point by showing that there are collections of languages that can be TxtFex2-identified by a team employing 6 machines, at least 5 of which are required to be successful, but cannnot be TxtFex2-identified by any single machine. Additionally, aggregation ratios are also derived for finite identification of languages from positive data and for numerous criteria involving language learning from both positive and negative data.
30890449
Prudence in Vacillatory Language Identification (Extended Abstract)
The present paper settles an open question about ‘prudent’ vacillatory identification of grammars from positive data only.
16978245
Learning with the Knowledge of an Upper Bound on Program Size
Abstract Two learning situations are considered: machine identification of programs from graphs of recursive functions (modeling inductive hypothesis formation) and machine identification of grammars from texts of recursively enumerable languages (modeling first language acquisition). Both these learning models are extended to account for situations in which a learning machine is provided additional information in the form of knowledge about an upper bound on the minimal size program (grammar) for the function (language) being identified. For a number of such extensions, it is shown that larger classes of functions (languages) can be algorithmically identified in the presence of upper bound information. Numerous interesting relationships are shown between different models of learning, number of anomalies allowed in the inferred program (grammar), and number of anomalies allowed in the upper bound information.
16032991
Not-So-Nearly-Minimal-Size Program Inference
Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and “nearly” minimal size, i.e, within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs severely limits learning power. Nonetheless, in, for example, scientific inference, parsimony is considered highly desirable. A limcomputable function is (by definition) one computable by a procedure allowed to change its mind finitely many times about its output. Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be “not-so-nearly” minimal size, e.g.; to be within a lim-computable function of actual minimal size. It is interestingly shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Also considered are lim-computable functions as above but for which notations for constructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal complexity bounded version of lim-computability, the power of the resultant learning criteria form strict infinite hierarchies intermediate between the computable and the lim-computable cases. Many open questions are also presented.
7521284
On learning to coordinate: random bits help, insightful normal forms, and competency isomorphisms
A mere bounded number of random bits judiciously employed by a probabilistically correct algorithmic coordinator is shown to increase the power of learning to coordinate compared to deterministic algorithmic coordinators. Furthermore, these probabilistic algorithmic coordinators are provably not characterized in power by teams of deterministic ones. An insightful, enumeration technique based, normal form characterization of the classes that are learnable by total computable coordinators is given. These normal forms are for insight only since it is shown that the complexity of the normal form of a total computable coordinator can be infeasible compared to the original coordinator. Montagna and Osherson showed that the competence class of a total coordinator cannot be strictly improved by another total coordinator. It is shown in the present paper that the competencies of any two total coordinators are the same modulo isomorphism. Furthermore, a completely effective, index set version of this competency isomorphism result is given, where all the coordinators are total computable. We also investigate the competence classes of total coordinators from the points of view of topology and descriptive set theory.
1156882
Analytic evaluation of the expectation and variance of different performance measures of a schedule on a single machine under processing time variability
Abstract
In this paper, we present closed-form expressions, wherever possible, or devise algorithms otherwise, to determine the expectation and variance of a given schedule on a single machine. We consider a variety of completion time and due date-based objectives. The randomness in the scheduling process is due to variable processing times with known means and variances of jobs and, in some cases, a known underlying processing time distribution. The results that we present in this paper can enable evaluation of a schedule in terms of both the expectation and variance of a performance measure considered, and thereby, aid in obtaining a stable schedule. Additionally, the expressions and algorithms that are presented, can be incorporated in existing scheduling algorithms in order to determine expectation-variance efficient schedules.

30649473
Joint Bidding in the Name-Your-Own-Price Channel: A Strategic Analysis
In this paper, we study the name-your-own-price (NYOP) channel. We examine theoretically and empirically whether asking consumers to place a joint bid for multiple items, rather than bid one item at a time as practiced today, can increase NYOP retailers' profits. Relatedly, we also examine whether allowing consumers to self-select whether to place a joint bid or itemwise bids increases retailers' profits and consumers' surplus. We construct a dynamic model that incorporates both demand uncertainty and supply uncertainty to address these issues. Our theoretical analysis identifies the conditions under which joint bidding can increase both NYOP retailers' profits and consumers' surplus. We find that some consumers might bid more for the very same items when they place joint bids. The increase in bid amount is related to the fact that joint bidding reduces the chance of mismatch between NYOP retailers' costs and consumer bids. We conducted a laboratory study to assess the descriptive validity of some of the model predictions, because there are no field data on joint bidding in the NYOP channel. The results of the study are directionally consistent with our theory.
120386960
Evolutionary games with two timescales
We consider a two timescale model of learning by economic agents wherein active or 'ontogenetic' learning by individuals takes place on a fast scale and passive or 'phylogenetic' learning by society as a whole on a slow scale, each affecting the evolution of the other. The former is modelled by the Monte Carlo dynamics of physics, while the latter is modelled by the replicator dynamics of evolutionary biology. Various qualitative aspects of the dynamics are studied in some simple cases, both analytically and numerically, and its role as a useful modelling device is emphasized.
15127807
Pricing of Information Products on Online Servers: Issues, Models, and Analysis
Online information servers that provide access to diverse databases where users can search for, browse through, and download the information they need have been rapidly increasing in number in the past few years. Online vendors have traditionally charged users for information on the based on the length of the time they were connected to the databases. With hardware and software advances, many online servers have recently started changing their pricing strategies to search-based and/or subscription-fee pricing. This paper examines the various issues involved in pricing these information products, and presents an economic approach to analyze conditions under which the various pricing schemes may prove optimal for the online servers. Our results show that the variation in consumer expertise and valuation of information affects the choice of a pricing strategy by the server. We present general conditions under which subscription-fee pricing is optimal even when consumer demand is inelastic. We also find that, given the cost structures characterizing the market, undifferentiated online servers can compete and coexist in the market each making positive profits. We show that in a competitive setting an increase in costs of online servers can sometimes benefit them by enabling them to differentiate themselves. Our results offer insights into the trends in pricing strategies and may provide an explanation as to why many servers may persist with connect-time strategies.
10615305
Manufacturing sypply chain management: distributed supply chain simulation across enterprise boundaries
The effective practice of supply chain management (SCM) is crucial to improve corporations' competitive advantage. Many corporations have built simulation models to facilitate the application of simulation in designing, evaluating, and optimizing their supply chain. Traditionally, a supply chain involves only a single enterprise with multiple facilities and distribution centers. Hence, sharing of detailed simulation models is not a problem in this scenario. But in recent years, the scope of SCM has evolved to cross the enterprise boundaries. Applying simulation in designing, evaluating, and optimizing the supply chain becomes more difficult since the participating corporations might not be willing to share their simulation models with partners. In this paper, distributed simulation techniques are presented as an enabling technology that allows corporations to construct a cross enterprise simulation while hiding model details within the enterprise. This can be realized by either building the simulation on top of the Runtime Infrastructure of the High Level Architecture or building the simulation on top of a customized distributed discrete event simulation protocol. These alternative approaches are compared in terms of their performance and interoperability. The comparison of the performance is done through a benchmarking test of a semiconductor supply chain model.