Integrated urban evolutionary modeling

Cellular automata models have proved rather popular as frameworks for simulating the physical growth of cities. Yet their brief history has been marked by a lack of application to real policy contexts, notwithstanding their obvious relevance to topical problems such as urban sprawl. Traditional urban models which emphasize transportation and demography continue to prevail despite their limitations in simulating realistic urban dynamics. To make progress, it is necessary to link CA models to these more traditional forms, focusing on the explicit simulation of the socio-economic attributes of land use activities as well as spatial interaction. There are several ways of tackling this but all are based on integration using various forms of strong and loose coupling which enable generically different models to be connected. Such integration covers many different features of urban simulation from data and software integration to internet operation, from interposing demand with the supply of urban land to enabling growth, location, and distributive mechanisms within such models to be reconciled. Here we will focus on developin

Complexity in city systems: Understanding, evolution, and design

6.4 Exemplars of complex systems There are many signatures of complexity revealed in the space-time patterning of cities (Batty, 2005) and here we will indicate three rather different but nevertheless linked exemplars. Our first deals with ..

Constant-Factor FPT Approximation for Capacitated k-Median

Capacitated k-median is one of the few outstanding optimization problems for which the existence of a polynomial time constant factor approximation algorithm remains an open problem. In a series of recent papers algorithms producing solutions violating either the number of facilities or the capacity by a multiplicative factor were obtained. However, to produce solutions without violations appears to be hard and potentially requires different algorithmic techniques. Notably, if parameterized by the number of facilities k, the problem is also W[2] hard, making the existence of an exact FPT algorithm unlikely. In this work we provide an FPT-time constant factor approximation algorithm preserving both cardinality and capacity of the facilities. The algorithm runs in time 2^O(k log k) n^O(1) and achieves an approximation ratio of 7+epsilon

Tight Kernel Bounds for Problems on Graphs with Small Degeneracy

In this paper we consider kernelization for problems on d-degenerate graphs, i.e. graphs such that any subgraph contains a vertex of degree at most $d$. This graph class generalizes many classes of graphs for which effective kernelization is known to exist, e.g. planar graphs, H-minor free graphs, and H-topological-minor free graphs. We show that for several natural problems on d-degenerate graphs the best known kernelization upper bounds are essentially tight.Comment: Full version of ESA 201

Dynamics of urban sprawl

This paper introduces a framework for understanding the dynamics of urban growth,particularly the continuing problem of urban sprawl. The models we present are based on transitions from vacant land to established development. We propose that the essential mechanism of transition is analogous to the way an epidemic is generated within a susceptible population, with waves of development being generated from the conversion of available land to new development and redevelopment through the aging process. We first outline the standard aggregate model in differential equation form, showing how different variants (including logistic, exponential, predator-prey models) can be derived for various urban growth situations. We then generalize the model to a spatial system and show how sprawl can be conceived as a process of both interaction/reaction and diffusion. We operationalize the model as a cellular automata (CA) which implies that diffusion is entirely local, and we then illustrate how waves of development and redevelopment characterizing both sprawl and aging of the existing urban stock, can be simulated.Finally we show how the model can be adapted to a real urban situation - the AnnArbor area in Eastern Michigan - where we demonstrate how waves of development are absorbed and modified by particular historical contingencies associated with the re-existing urban structure

On the Cost of Essentially Fair Clusterings

Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters -- especially if the data is already biased. At NIPS 2017, Chierichetti et al. proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both a 4-approximation for the fair $k$-center problem and a $O(t)$-approximation for the fair $k$-median problem, where $t$ is a parameter for the fairness model. For multiple protected classes, the best known result is a 14-approximation for fair $k$-center. We extend and improve the known results. Firstly, we give a 5-approximation for the fair $k$-center problem with multiple protected classes. Secondly, we propose a relaxed fairness notion under which we can give bicriteria constant-factor approximations for all of the classical clustering objectives $k$-center, $k$-supplier, $k$-median, $k$-means and facility location. The latter approximations are achieved by a framework that takes an arbitrary existing unfair (integral) solution and a fair (fractional) LP solution and combines them into an essentially fair clustering with a weakly supervised rounding scheme. In this way, a fair clustering can be established belatedly, in a situation where the centers are already fixed

Privacy Preserving Clustering with Constraints

The k-center problem is a classical combinatorial optimization problem which asks to find k centers such that the maximum distance of any input point in a set P to its assigned center is minimized. The problem allows for elegant 2-approximations. However, the situation becomes significantly more difficult when constraints are added to the problem. We raise the question whether general methods can be derived to turn an approximation algorithm for a clustering problem with some constraints into an approximation algorithm that respects one constraint more. Our constraint of choice is privacy: Here, we are asked to only open a center when at least l clients will be assigned to it. We show how to combine privacy with several other constraints