Multi-Budgeted Directed Cuts

In this paper, we study multi-budgeted variants of the classic minimum cut problem and graph separation problems that turned out to be important in parameterized complexity: Skew Multicut and Directed Feedback Arc Set. In our generalization, we assign colors 1,2,...,l to some edges and give separate budgets k_1,k_2,...,k_l for colors 1,2,...,l. For every color i in {1,...,l}, let E_i be the set of edges of color i. The solution C for the multi-budgeted variant of a graph separation problem not only needs to satisfy the usual separation requirements (i.e., be a cut, a skew multicut, or a directed feedback arc set, respectively), but also needs to satisfy that |C cap E_i| <= k_i for every i in {1,...,l}. Contrary to the classic minimum cut problem, the multi-budgeted variant turns out to be NP-hard even for l = 2. We propose FPT algorithms parameterized by k=k_1 +...+ k_l for all three problems. To this end, we develop a branching procedure for the multi-budgeted minimum cut problem that measures the progress of the algorithm not by reducing k as usual, by but elevating the capacity of some edges and thus increasing the size of maximum source-to-sink flow. Using the fact that a similar strategy is used to enumerate all important separators of a given size, we merge this process with the flow-guided branching and show an FPT bound on the number of (appropriately defined) important multi-budgeted separators. This allows us to extend our algorithm to the Skew Multicut and Directed Feedback Arc Set problems. Furthermore, we show connections of the multi-budgeted variants with weighted variants of the directed cut problems and the Chain l-SAT problem, whose parameterized complexity remains an open problem. We show that these problems admit a bounded-in-parameter number of "maximally pushed" solutions (in a similar spirit as important separators are maximally pushed), giving somewhat weak evidence towards their tractability

Multi-budgeted Directed Cuts

In this paper, we study multi-budgeted variants of the classic minimum cut problem and graph separation problems that turned out to be important in parameterized complexity: SKEW MULTICUT and DIRECTED FEEDBACK ARC SET. In our generalization, we assign colors 1, 2,..., l to some edges and give separate budgets k(1), k(2),..., k(l) for colors 1, 2,..., l. For every color i is an element of {1,..., l}, let E-i be the set of edges of color i. The solution C for the multi-budgeted variant of a graph separation problem not only needs to satisfy the usual separation requirements (i.e., be a cut, a skew multicut, or a directed feedback arc set, respectively), but also needs to satisfy that vertical bar C boolean AND E-i vertical bar <= k(i) for every i is an element of {1,..., l}. Contrary to the classic minimum cut problem, the multi-budgeted variant turns out to be NP-hard even for l = 2. We propose FPT algorithms parameterized by k = k(1) + ... + k(l) for all three problems. To this end, we develop a branching procedure for the multi-budgeted minimum cut problem that measures the progress of the algorithm not by reducing k as usual, by but elevating the capacity of some edges and thus increasing the size of maximum source-to-sink flow. Using the fact that a similar strategy is used to enumerate all important separators of a given size, we merge this process with the flow-guided branching and show an FPT bound on the number of (appropriately defined) important multi-budgeted separators. This allows us to extend our algorithm to the Skew Multicut and Directed Feedback Arc Set problems. Furthermore, we show connections of the multi-budgeted variants with weighted variants of the directed cut problems and the Chain l-SATproblem, whose parameterized complexity remains an open problem. We show that these problems admit a bounded-in-parameter number of "maximally pushed" solutions (in a similar spirit as important separators are maximally pushed), giving somewhat weak evidence towards their tractability

Milwaukee County-Funded Parks and Cultural Institutions

The Public Policy Forum's role in the Audit of Greater Milwaukee's Regional Cultural Assets was to examine the fiscal condition of those cultural assets owned and/or funded by Milwaukee County: the Milwaukee Public Museum, Marcus Center for the Performing Arts, Milwaukee County War Memorial Center, Milwaukee County Historical Society, Charles Allis Museum, Villa Terrace Decorative Art Museum, Milwaukee County Cultural Artistic and Musical Programming Advisory Council, Milwaukee County Zoo and Milwaukee County Parks

Fiscal Renaissance in a Democratic South Africa

South Africa has overcome adverse initial conditions to achieve a remarkable fiscal transformation since the 1994 democratic elections, held amid uncertainty about its ability to maintain the rule of law and resist the populist spending pressures. Constitutionally-bases, durable and credible fiscal reforms have contained spending and rendered policy at all levels of government more transparent and accountable, and more predictable through multi-year budgeting. Extensive tax reform and more efficient tax collection has expanded revenue, permitting lower tax rates for both individuals and companies, and personal tax relief. Fiscal consolidation almost eliminated the budget deficit by 2005, and with improved debt management, has created a lower and more sustainable debt burden. While highly centralised revenue raising powers and greater decentralisation of expenditure to sub-national governments created a vertical fiscal imbalance, a strict no-bail out approach helped control provincial spending. The fiscal-monetary policy mix has stabilised the macro-economy and reduced uncertainty, reflected internationally in narrowed sovereign risk spreads and improved debt ratings. However, micro-service delivery in social expenditure has been disappointing (in some cases due to capacity constraints rather than inadequate fiscal allocations). And long-term decline in infrastructure investment and capital stock is only belatedly receiving attention. The challenge is to increase social and infrastructure expenditure at a sustainable rate and to improve the quality of service delivery, to avoid undermining the gains in microeconomic stability.

On a generalization of iterated and randomized rounding

We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack, there is a randomized procedure that returns an integral solution that satisfies the guarantees of iterated rounding and also has concentration properties. We use this to give new results for several classic problems where iterated rounding has been useful

Variance analysis and linear contracts in agencies with distorted performance measures

This paper investigates the role of variance analysis procedures in aligning objectives under the condition of distorted performance measurement. A riskneutral agency with linear contracts is analyzed, whereby the agent receives postcontract, pre-decision information on his productivity. If the performance measure is informative with respect to the agent’s marginal product concerning the principal’s objective, variance investigation can alleviate effort misallocation. These results carry over to a participative budgeting situation, but in this case the variance investigation procedures are less demanding

Child of the Long Take: Alfonso Cuaron\u27s Film Aesthetics in the Shadow of Globalization

Alfonso Cuaron\u27s 2006 film, Children of Men, not only suggests that the economic pressures on contemporary Hollywood directors differ little from those in the studio era, it also suggests that film style in the age of globalization is not as homogenized as many fear. The long take is the most prominent feature in Children of Men, including many which are digitally contrived. Lofty reasons by the filmmakers are given for these long lakes, but there are more pedestrian reasons behind this. Other examples past and present suggest that often the tong take serves the needs of both filmmakers and their producers, at least for awhile. Cuaron himself paid his dues over the years with more generic films, and is now making a bold auteurist declaration with these long takes. The question remains whether the economics of Hollywood will allow him to continue

Non-Uniform Robust Network Design in Planar Graphs

Robust optimization is concerned with constructing solutions that remain feasible also when a limited number of resources is removed from the solution. Most studies of robust combinatorial optimization to date made the assumption that every resource is equally vulnerable, and that the set of scenarios is implicitly given by a single budget constraint. This paper studies a robustness model of a different kind. We focus on \textbf{bulk-robustness}, a model recently introduced~\cite{bulk} for addressing the need to model non-uniform failure patterns in systems. We significantly extend the techniques used in~\cite{bulk} to design approximation algorithm for bulk-robust network design problems in planar graphs. Our techniques use an augmentation framework, combined with linear programming (LP) rounding that depends on a planar embedding of the input graph. A connection to cut covering problems and the dominating set problem in circle graphs is established. Our methods use few of the specifics of bulk-robust optimization, hence it is conceivable that they can be adapted to solve other robust network design problems.Comment: 17 pages, 2 figure