Competitive Boolean Function Evaluation: Beyond Monotonicity, and the Symmetric Case

We study the extremal competitive ratio of Boolean function evaluation. We provide the first non-trivial lower and upper bounds for classes of Boolean functions which are not included in the class of monotone Boolean functions. For the particular case of symmetric functions our bounds are matching and we exactly characterize the best possible competitiveness achievable by a deterministic algorithm. Our upper bound is obtained by a simple polynomial time algorithm.Comment: 15 pages, 1 figure, to appear in Discrete Applied Mathematic

The Landscape of Salesforce for Nonprofits: A Report on the Current Marketplace for Apps

Do you use Salesforce as a Constituent Relationship Management database at your organization, or are you considering it? Since it launched in 1999, more than 20,000 nonprofits have employed the cloud-based system, which is made available to them for free through the philanthropic Salesforce Foundation. What's the catch? Making such a powerful system work for the particular needs of a nonprofit isn't always straightforward. This report can tell you everything you need to know.What's in it? To learn more about the benefits and drawbacks of Salesforce, we interviewed nine prominent consultants specializing in implementing Salesforce for nonprofits along with several members of the Salesforce.com Foundation about what the platform does well, and what you'll want to add to it to suit your needs. We evaluated some of the constituent management packages built on top of Salesforce, including the Salesforce Foundation's Nonprofit Starter Pack, which is aimed at turning the sales automation platform into a tool for nonprofits. We also took a look at the universe of add-ons to the base Salesforce platform -- called "apps" because of Salesforce's online marketplace, the App Exchange -- to find out which might be useful to support a nonprofit's processes.The goal for this report was to break down misconceptions about the tool and to collect disparate information in one place to help you make informed decisions. Whether you're already using Salesforce, are thinking about adopting it, or have yet to even consider it, there's information here for you.What's more, we've included a directory of consultants or firms with experience working with nonprofits to implement Salesforce and the additional App Exchange modules that we cover in this report to make it easier for you to find the help you'll need

Combinatorial Assortment Optimization

Assortment optimization refers to the problem of designing a slate of products to offer potential customers, such as stocking the shelves in a convenience store. The price of each product is fixed in advance, and a probabilistic choice function describes which product a customer will choose from any given subset. We introduce the combinatorial assortment problem, where each customer may select a bundle of products. We consider a model of consumer choice where the relative value of different bundles is described by a valuation function, while individual customers may differ in their absolute willingness to pay, and study the complexity of the resulting optimization problem. We show that any sub-polynomial approximation to the problem requires exponentially many demand queries when the valuation function is XOS, and that no FPTAS exists even for succinctly-representable submodular valuations. On the positive side, we show how to obtain constant approximations under a "well-priced" condition, where each product's price is sufficiently high. We also provide an exact algorithm for $k$-additive valuations, and show how to extend our results to a learning setting where the seller must infer the customers' preferences from their purchasing behavior

Toward a Social Practice Theory of Relational Competing

This paper brings together the competitive dynamics and strategy-aspractice literatures to investigate relational competition. Drawing on a global ethnography of the reinsurance market, we develop the concept of micro-competitions, which are the focus of competitors’ everyday competitive practices. We find variation in relational or rivalrous competition by individual competitors across the phases of a micro-competition, between competitors within a micro-competition, and across multiple micro-competitions. These variations arise from the interplay between the unfolding competitive arena and the implementation of each firm’s strategic portfolio. We develop a conceptual framework that makes four contributions to: relational competition; reconceptualizing action and response; elaborating on the awareness-motivation-capability framework within competitive dynamics; and the recursive dynamic by which implementing strategy inside firms shapes, and is shaped by, the competitive arena

An Expressive Language and Efficient Execution System for Software Agents

Software agents can be used to automate many of the tedious, time-consuming information processing tasks that humans currently have to complete manually. However, to do so, agent plans must be capable of representing the myriad of actions and control flows required to perform those tasks. In addition, since these tasks can require integrating multiple sources of remote information ? typically, a slow, I/O-bound process ? it is desirable to make execution as efficient as possible. To address both of these needs, we present a flexible software agent plan language and a highly parallel execution system that enable the efficient execution of expressive agent plans. The plan language allows complex tasks to be more easily expressed by providing a variety of operators for flexibly processing the data as well as supporting subplans (for modularity) and recursion (for indeterminate looping). The executor is based on a streaming dataflow model of execution to maximize the amount of operator and data parallelism possible at runtime. We have implemented both the language and executor in a system called THESEUS. Our results from testing THESEUS show that streaming dataflow execution can yield significant speedups over both traditional serial (von Neumann) as well as non-streaming dataflow-style execution that existing software and robot agent execution systems currently support. In addition, we show how plans written in the language we present can represent certain types of subtasks that cannot be accomplished using the languages supported by network query engines. Finally, we demonstrate that the increased expressivity of our plan language does not hamper performance; specifically, we show how data can be integrated from multiple remote sources just as efficiently using our architecture as is possible with a state-of-the-art streaming-dataflow network query engine

Information-based complexity, feedback and dynamics in convex programming

We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an {\em oracle} for noisy information about the unknown objective function, and the goal is to (approximately) minimize every function in a given class using as few queries as possible. We show that, in order for a function to be optimized, the algorithm must be able to accumulate enough information about the objective. This, in turn, puts limits on the speed of optimization under specific assumptions on the oracle and the type of feedback. Our techniques are akin to the ones used in statistical literature to obtain minimax lower bounds on the risks of estimation procedures; the notable difference is that, unlike in the case of i.i.d. data, a sequential optimization algorithm can gather observations in a {\em controlled} manner, so that the amount of information at each step is allowed to change in time. In particular, we show that optimization algorithms often obey the law of diminishing returns: the signal-to-noise ratio drops as the optimization algorithm approaches the optimum. To underscore the generality of the tools, we use our approach to derive fundamental lower bounds for a certain active learning problem. Overall, the present work connects the intuitive notions of information in optimization, experimental design, estimation, and active learning to the quantitative notion of Shannon information.Comment: final version; to appear in IEEE Transactions on Information Theor

An Algorithm for Bichromatic Sorting with Polylog Competitive Ratio

The problem of sorting with priced information was introduced by [Charikar, Fagin, Guruswami, Kleinberg, Raghavan, Sahai (CFGKRS), STOC 2000]. In this setting, different comparisons have different (potentially infinite) costs. The goal is to find a sorting algorithm with small competitive ratio, defined as the (worst-case) ratio of the algorithm's cost to the cost of the cheapest proof of the sorted order. The simple case of bichromatic sorting posed by [CFGKRS] remains open: We are given two sets $A$ and $B$ of total size $N$, and the cost of an $A-A$ comparison or a $B-B$ comparison is higher than an $A-B$ comparison. The goal is to sort $A \cup B$. An $\Omega(\log N)$ lower bound on competitive ratio follows from unit-cost sorting. Note that this is a generalization of the famous nuts and bolts problem, where $A-A$ and $B-B$ comparisons have infinite cost, and elements of $A$ and $B$ are guaranteed to alternate in the final sorted order. In this paper we give a randomized algorithm InversionSort with an almost-optimal w.h.p. competitive ratio of $O(\log^{3} N)$. This is the first algorithm for bichromatic sorting with a $o(N)$ competitive ratio.Comment: 18 pages, accepted to ITCS 2024. arXiv admin note: text overlap with arXiv:2211.0460