Matchings with lower quotas: Algorithms and complexity

We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G=(A∪˙P,E)G=(A∪˙P,E) with weights on the edges in E, and with lower and upper quotas on the vertices in P. We seek a maximum weight many-to-one matching satisfying two sets of constraints: vertices in A are incident to at most one matching edge, while vertices in P are either unmatched or they are incident to a number of matching edges between their lower and upper quota. This problem, which we call maximum weight many-to-one matching with lower and upper quotas (WMLQ), has applications to the assignment of students to projects within university courses, where there are constraints on the minimum and maximum numbers of students that must be assigned to each project. In this paper, we provide a comprehensive analysis of the complexity of WMLQ from the viewpoints of classical polynomial time algorithms, fixed-parameter tractability, as well as approximability. We draw the line between NPNP-hard and polynomially tractable instances in terms of degree and quota constraints and provide efficient algorithms to solve the tractable ones. We further show that the problem can be solved in polynomial time for instances with bounded treewidth; however, the corresponding runtime is exponential in the treewidth with the maximum upper quota umaxumax as basis, and we prove that this dependence is necessary unless FPT=W[1]FPT=W[1]. The approximability of WMLQ is also discussed: we present an approximation algorithm for the general case with performance guarantee umax+1umax+1, which is asymptotically best possible unless P=NPP=NP. Finally, we elaborate on how most of our positive results carry over to matchings in arbitrary graphs with lower quotas

Matchings with lower quotas : algorithms and complexity

We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G=(A∪˙P,E) with weights on the edges in E, and with lower and upper quotas on the vertices in P. We seek a maximum weight many-to-one matching satisfying two sets of constraints: vertices in A are incident to at most one matching edge, while vertices in P are either unmatched or they are incident to a number of matching edges between their lower and upper quota. This problem, which we call maximum weight many-to-one matching with lower and upper quotas (WMLQ), has applications to the assignment of students to projects within university courses, where there are constraints on the minimum and maximum numbers of students that must be assigned to each project. In this paper, we provide a comprehensive analysis of the complexity of WMLQ from the viewpoints of classical polynomial time algorithms, fixed-parameter tractability, as well as approximability. We draw the line between NP-hard and polynomially tractable instances in terms of degree and quota constraints and provide efficient algorithms to solve the tractable ones. We further show that the problem can be solved in polynomial time for instances with bounded treewidth; however, the corresponding runtime is exponential in the treewidth with the maximum upper quota umax as basis, and we prove that this dependence is necessary unless FPT=W[1]. The approximability of WMLQ is also discussed: we present an approximation algorithm for the general case with performance guarantee umax+1, which is asymptotically best possible unless P=NP. Finally, we elaborate on how most of our positive results carry over to matchings in arbitrary graphs with lower quotas

Many-to-one matchings with lower quotas : algorithms and complexity

We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G = (AUP,E) with weights on the edges in E, and with lower and upper quotas on the vertices in P. We seek a maximum weight many-toone matching satisfying two sets of constraints: vertices in A are incident to at most one matching edge, while vertices in P are either unmatched or they are incident to a number of matching edges between their lower and upper quota. This problem, which we call maximum weight many-toone matching with lower and upper quotas (wmlq), has applications to the assignment of students to projects within university courses, where there are constraints on the minimum and maximum numbers of students that must be assigned to each project. In this paper, we provide a comprehensive analysis of the complexity of wmlq from the viewpoints of classic polynomial time algorithms, fixed-parameter tractability, as well as approximability. We draw the line between NP-hard and polynomially tractable instances in terms of degree and quota constraints and provide efficient algorithms to solve the tractable ones. We further show that the problem can be solved in polynomial time for instances with bounded treewidth; however, the corresponding runtime is exponential in the treewidth with the maximum upper quota umax as basis, and we prove that this dependence is necessary unless FPT = W[1]. Finally, we also present an approximation algorithm for the general case with performance guarantee umax+1, which is asymptotically best possible unless P = NP

The Teleserye Story: Three Periods of the Evolution of the Filipino TV Soap Opera

The essay chronicles the history of the teleserye or the Filipino TV soap opera, one of today’s transnational televisual products making waves in different parts of the globe. It covers three periods—the period of transition from radio to TV (1962 to 1986), the period of competition (1986-2000), and the period of transformation (2000-present). Traversing through 60 years of the form’s enduring presence in Philippine television, it traces the format’s beginnings as it was introduced to the medium in a highly volatile social environment, and assesses its continued flourishing in democratized, contemporary times and consequent entry into the highly competitive global drama market, where it serves both foreign and its very own Filipino diasporic audiences. The essay echoes the abiding thesis of my studies about the cultural history of the teleserye—that the form is indeed the drama of Filipino life. As domestic, serial form, the teleserye’s intimate relation to the Filipino everyday ultimately makes it reflective of the country’s life and times, its evolution interconnected with the ebb and flow of Philippine history. These are illustrated by representative texts from the said periods, as well as key contexts that unravel the evolution of the form, now gleaned from a global, as well as diasporic context

Serial payers, serial losers? The political economy of Argentina's public debt

Background of INCASI Project H2020-MSCA-RISE-2015 GA 691004. WP1: CompilationA global neoliberal architecture has enabled many countries to increase their public debts to meet their fiscal needs. But since 2008 a number of European and North American economies have faced financial crises induced by unsustainable debts. This paper analyses the case of post-default Argentina since 2001, so as to better comprehend the political economy of public debt, especially in cases where governments are elected on anti-austerity platforms. Presidents Néstor and Cristina Kirchner were committed to a debt-reduction policy, yet Argentina faced a new,'selective', default in 2014. This paper analyses how the country has been trapped in a cycle of debt dependency, which can only be interrupted by a comprehensive audit of the debts legitimacy followed by debt cancellation. Critical lessons are provided for other countries facing similar situations

Serial payers, serial losers? The political economy of Argentina's public debt

Global neoliberal architecture has allowed countries to increase their debts to meet their needs. But ever since 2008, many European and North American countries have faced financial crises induced by unsustainable debts. This paper analyses the case of post-default Argentina since 2001, so as to better comprehend the political economy of public debt, especially in cases where governments are elected on anti-austerity platforms. Presidents Néstor and Cristina Kirchner were committed to a debt-reduction policy. Yet, Argentina faced a new, ‘selective’ default in 2014. This paper analyses why the country has inevitably trapped itself in a cycle of debt-dependency, which can only by interrupted by a comprehensive audit of its legitimacy followed by debt cancellation. Critical lessons are provided for other countries facing similar situations