612 research outputs found
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
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
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
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COMPLEXITY&APPROXIMABILITY OF QUANTIFIED&STOCHASTIC CONSTRAINT SATISFACTION PROBLEMS
Let D be an arbitrary (not necessarily finite) nonempty set, let C be a finite set of constant symbols denoting arbitrary elements of D, and let S and T be an arbitrary finite set of finite-arity relations on D. We denote the problem of determining the satisfiability of finite conjunctions of relations in S applied to variables (to variables and symbols in C) by SAT(S) (by SATc(S).) Here, we study simultaneously the complexity of decision, counting, maximization and approximate maximization problems, for unquantified, quantified and stochastically quantified formulas. We present simple yet general techniques to characterize simultaneously, the complexity or efficient approximability of a number of versions/variants of the problems SAT(S), Q-SAT(S), S-SAT(S),MAX-Q-SAT(S) etc., for many different such D,C ,S, T. These versions/variants include decision, counting, maximization and approximate maximization problems, for unquantified, quantified and stochastically quantified formulas. Our unified approach is based on the following two basic concepts: (i) strongly-local replacements/reductions and (ii) relational/algebraic represent ability. Some of the results extend the earlier results in [Pa85,LMP99,CF+93,CF+94O]u r techniques and results reported here also provide significant steps towards obtaining dichotomy theorems, for a number of the problems above, including the problems MAX-&-SAT( S), and MAX-S-SAT(S). The discovery of such dichotomy theorems, for unquantified formulas, has received significant recent attention in the literature [CF+93,CF+94,Cr95,KSW97
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Complexity of analysis and verification problems for communicating automata and discrete dynamical systems.
We identify several simple but powerful concepts, techniques, and results; and we use them to characterize the complexities of a number of basic problems II, that arise in the analysis and verification of the following models M of communicating automata and discrete dynamical systems: systems of communicating automata including both finite and infinite cellular automata, transition systems, discrete dynamical systems, and succinctly-specified finite automata. These concepts, techniques, and results are centered on the following: (1) reductions Of STATE-REACHABILITY problems, especially for very simple systems of communicating copies of a single simple finite automaton, (2) reductions of generalized CNF satisfiability problems [Sc78], especially to very simple communicating systems of copies of a few basic acyclic finite sequential machines, and (3) reductions of the EMPTINESS and EMPTINESS-OF-INTERSECTION problems, for several kinds of regular set descriptors. For systems of communicating automata and transition systems, the problems studied include: all equivalence relations and simulation preorders in the Linear-time/Branching-time hierarchies of equivalence relations and simulation preorders of [vG90, vG93], both without and with the hiding abstraction. For discrete dynamical systems, the problems studied include the INITIAL and BOUNDARY VALUE PROBLEMS (denoted IVPs and BVPs, respectively), for nonlinear difference equations over many different algebraic structures, e.g. all unitary rings, all finite unitary semirings, and all lattices. For succinctly specified finite automata, the problems studied also include the several problems studied in [AY98], e.g. the EMPTINESS, EMPTINESS-OF-INTERSECTION, EQUIVALENCE and CONTAINMENT problems. The concepts, techniques, and results presented unify and significantly extend many of the known results in the literature, e.g. [Wo86, Gu89, BPT91, GM92, Ra92, HT94, SH+96, AY98, AKY99, RH93, SM73, Hu73, HRS76, HR78], for communicating automata including both finite and infinite cellular automata and for finite automata specified by special kinds of context-free grammars, by regular operations augmented with squaring and intersection, and specified succinctly as in [AY98, AKY99]. Moreover, our development of these concepts, techniques, and results shows how several ideas, techniques, and results, for the individual models M above can be extended to apply to all or to most of these models. As one example of this and paraphrasing [BPTBl] , we show that most of these models M exhibit computationally-intractable sensitive dependence on initial conditions, for the same reason. These computationally-intractable sensitivities range from PSPACE-hard to undecidable
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