Bicriteria Network Design Problems

We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first, find a <subgraph \from a given subgraph-class that minimizes the second objective subject to the budget on the first. We consider three different criteria - the total edge cost, the diameter and the maximum degree of the network. Here, we present the first polynomial-time approximation algorithms for a large class of bicriteria network design problems for the above mentioned criteria. The following general types of results are presented. First, we develop a framework for bicriteria problems and their approximations. Second, when the two criteria are the same %(note that the cost functions continue to be different) we present a ``black box'' parametric search technique. This black box takes in as input an (approximation) algorithm for the unicriterion situation and generates an approximation algorithm for the bicriteria case with only a constant factor loss in the performance guarantee. Third, when the two criteria are the diameter and the total edge costs we use a cluster-based approach to devise a approximation algorithms --- the solutions output violate both the criteria by a logarithmic factor. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. We show how these pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur

On the equivalence, containment, and covering problems for the regular and context-free languages

We consider the complexity of the equivalence and containment problems for regular expressions and context-free grammars, concentrating on the relationship between complexity and various language properties. Finiteness and boundedness of languages are shown to play important roles in the complexity of these problems. An encoding into grammars of Turing machine computations exponential in the size of the grammar is used to prove several exponential lower bounds. These lower bounds include exponential time for testing equivalence of grammars generating finite sets, and exponential space for testing equivalence of non-self-embedding grammars. Several problems which might be complex because of this encoding are shown to simplify for linear grammars. Other problems considered include grammatical covering and structural equivalence for right-linear, linear, and arbitrary grammars

Corporate political activity in the context of unhealthy food advertising restrictions across Transport for London:A qualitative case study

BACKGROUND: Diets with high proportions of foods high in fat, sugar, and/or salt (HFSS) contribute to malnutrition and rising rates of childhood obesity, with effects throughout the life course. Given compelling evidence on the detrimental impact HFSS advertising has on children’s diets, the World Health Organization unequivocally supports the adoption of restrictions on HFSS marketing and advertising. In February 2019, the Greater London Authority introduced novel restrictions on HFSS advertising across Transport for London (TfL), one of the most valuable out-of-home advertising estates. In this study, we examined whether and how commercial actors attempted to influence the development of these advertising restrictions. METHODS AND FINDINGS: Using requests under the Freedom of Information Act, we obtained industry responses to the London Food Strategy consultation, correspondence between officials and key industry actors, and information on meetings. We used an existing model of corporate political activity, the Policy Dystopia Model, to systematically analyse arguments and activities used to counter the policy. The majority of food and advertising industry consultation respondents opposed the proposed advertising restrictions, many promoting voluntary approaches instead. Industry actors who supported the policy were predominantly smaller businesses. To oppose the policy, industry respondents deployed a range of strategies. They exaggerated potential costs and underplayed potential benefits of the policy, for instance, warning of negative economic consequences and questioning the evidence underlying the proposal. Despite challenging the evidence for the policy, they offered little evidence in support of their own claims. Commercial actors had significant access to the policy process and officials through the consultation and numerous meetings, yet attempted to increase access, for example, in applying to join the London Child Obesity Taskforce and inviting its members to events. They also employed coalition management, engaging directly and through business associations to amplify their arguments. Some advertising industry actors also raised the potential of legal challenges. The key limitation of this study is that our data focused on industry–policymaker interactions; thus, our findings are unable to present a comprehensive picture of political activity. CONCLUSIONS: In this study, we identified substantial opposition from food and advertising industry actors to the TfL advertising restrictions. We mapped arguments and activities used to oppose the policy, which might help other public authorities anticipate industry efforts to prevent similar restrictions in HFSS advertising. Given the potential consequences of commercial influence in these kinds of policy spaces, public bodies should consider how they engage with industry actors

Self generated randomness, defect wandering and viscous flow in stripe glasses

We show that the competition between interactions on different length scales, as relevant for the formation of stripes in doped Mott insulators, can cause a glass transition in a system with no explicitly quenched disorder. We analytically determine a universal criterion for the emergence of an exponentially large number of metastable configurations that leads to a finite configurational entropy and a landscape dominated viscous flow. We demonstrate that glassines is unambiguously tied to a new length scale which characterizes the typical length over which defects and imperfections in the stripe pattern are allowed to wander over long times.Comment: 17 pages, 9 figure

Dynamical Mean Field Theory for Self-Generated Quantum Glasses

We present a many body approach for non-equilibrium behavior and self-generated glassiness in strongly correlated quantum systems. It combines the dynamical mean field theory of equilibrium systems with the replica theory for classical glasses without quenched disorder. We apply this approach to study a quantized version of the Brazovskii model and find a self-generated quantum glass that remains in a quantum mechanically mixed state as T -> 0. This quantum glass is formed by a large number of competing states spread over an energy region which is determined within our theory.Comment: 10 pages, 4 figure