Related papers: Greedy algorithms and Zipf laws
This paper is devoted to the theoretical study of the efficiency, namely, stability of some greedy algorithms. In the greedy approximation theory researchers are mostly interested in the following two important properties of an algorithm --…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
Classical optimization algorithms--hill climbing, simulated annealing, population-based methods--generate candidate solutions via random perturbations. We replace the random proposal generator with an LLM agent that reasons about evaluation…
In Hopenhayn's (1992) entry-exit model productivity is bounded, implying that the predicted firm size distribution cannot match the power law tail observable in the data. In this paper we remove the boundedness assumption and, in this more…
The submodular maximization problem is widely applicable in many engineering problems where objectives exhibit diminishing returns. While this problem is known to be NP-hard for certain subclasses of objective functions, there is a greedy…
We investigate rumor spreading in a generalized Maki-Thompson model with spontaneous stifling, evolving on quasi-transitive networks. Individuals are either ignorants, spreaders, or stiflers; spreaders stop by contact with other spreaders…
An analytical approach to network dynamics is used to show that when agents copy their state randomly the network arrives to a stationary status in which the distribution of states is independent of the agents degree. The effects of network…
A model of Boolean agents competing in a market is presented where each agent bases his action on information obtained from a small group of other agents. The agents play a competitive game that rewards those in the minority. After a long…
We analyze an ideal gas like models of a trading market. We propose a new fit for the money distribution in the fixed or uniform saving market. For the marketwith quenched random saving factors for its agents we show that the steady state…
We introduce a model of proportional growth to explain the distribution $P(g)$ of business firm growth rates. The model predicts that $P(g)$ is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an…
The derivation of the maximum entropy distribution of particles in boxes yields two kinds of distributions: a "bell-like" distribution and a long-tail distribution. The first one is obtained when the ratio between particles and boxes is…
We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest…
A service system with multiple types of arriving customers is considered. There is an infinite number of homogeneous servers. Multiple customers can be placed for simultaneous service into one server, subject to general packing constraints.…
The distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper we show that a thermodynamic model based on the Maximum Entropy Principle, with dynamical prior information, can be constructed that…
We consider a single-server system with service stations in each point of the circle. Customers arrive after exponential times at uniformly-distributed locations. The server moves at finite speed and adopts a greedy routing mechanism. It…
MapReduce has become the de facto standard model for designing distributed algorithms to process big data on a cluster. There has been considerable research on designing efficient MapReduce algorithms for clustering, graph optimization, and…
In times of plenty expectations rise, just as in times of crisis they fall. This can be mathematically described as a Win-Stay-Lose-Shift strategy with dynamic aspiration levels, where individuals aspire to be as wealthy as their average…
The time evolution of Earth with her cities, languages and countries is considered in terms of the multiplicative noise and the fragmentation- processes, where the related families, size distributions, lifetimes, bilinguals, etc. are…
We study a dynamic model of information provision. A state of nature evolves according to a Markov chain. An informed advisor decides how much information to provide to an uninformed decision maker, so as to influence his short-term…
The key idea of this model is that firms are the result of an evolutionary process. Based on demand and supply considerations the evolutionary model presented here derives explicitly Gibrat's law of proportionate effects as the result of…