A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest

We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the Subtree Prune-and-Regraft (SPR) distance between two phylogenetic trees. Our result improves on the very recent 2.5-approximation algorithm due to Shi, Feng, You and Wang (2015). Our algorithm is the first approximation algorithm for this problem that uses LP duality in its analysis

Lessons from building paratransit operators’ capacity to be partners in Cape Town’s public transport reform process

In 2013 the Cape Town municipality initiated planning for the second phase of its MyCiTi bus system. The first phase, on which preparations commenced in 2007, relied on incorporating existing road-based operators in a bus rapid transit (BRT) system. The municipality under-estimated the cost and level of effort involved in the wholesale corporatisation of paratransit operators while concurrently equipping them to become BRT operators. Learning from this experience, it developed a more incremental transition approach in the second phase, the first fruit of which was a pilot express bus service launched in mid-2014. The pilot service contract also provided for a training programme for paratransit operators in the affected parts of the city to build their managerial and technical capacity. It was envisaged that programme participants would ultimately manage and run the long-term operating companies and contracts that would be established by the end of the three-year interim period. This article provides a critical review of the programme’s context, content and participant experiences after the conclusion of its first year. In broad terms the programme has made a positive contribution to paratransit participants’ understanding of the shortcomings of their current operations and why reform might be necessary, but much still remains to be done to enable them to fill their envisaged roles in future public transport operations. In view of growing interest in BRT installation in Sub-Saharan Africa lessons from Cape Town’s reform process offer both cautionary evidence and a potential mechanism for drawing existing operators in as partners in reform

Layers and Matroids for the Traveling Salesman's Paths

Gottschalk and Vygen proved that every solution of the subtour elimination linear program for traveling salesman paths is a convex combination of more and more restrictive "generalized Gao-trees". We give a short proof of this fact, as a layered convex combination of bases of a sequence of increasingly restrictive matroids. A strongly polynomial, combinatorial algorithm follows for finding this convex combination, which is a new tool offering polyhedral insight, already instrumental in recent results for the $s-t$ path TSP

Paratransit operators' participation in public transport reform in Cape Town: a qualitative investigation of their business aspirations and attitudes to reform

Includes bibliographical referencesThe South African government launched two public transport reform programmes in the last two decades to address generally declining services as well as specific problems with paratransit, the dominant service provider. One programme aims to incorporate paratransit in new bus-based networks in cities; the other is a national paratransit fleet renewal scheme. Cape Town is arguably most advanced with the former, and the first phase of its bus network is nearing completion. Paratransit operators have shown resistance to both programmes, yet there have been few efforts to gain direct insight into their views on their businesses or their attitudes to reform. It is thus difficult to identify reasons behind their unenthusiastic response, or to understand if revisions to the programmes might cause more operators to opt in. This research employed a case study strategy to investigate paratransit operators' business aspirations and needs in Cape Town, and to identify commonalities between their attitudes and the aims of the reform programmes to inform potential amendments to these programmes. The details of incorporating paratransit operators in the new bus system in Cape Town were not systematically recorded, and it was thus first necessary to trace the engagement process between the municipality and these operators. Information was drawn from a variety of sources over a six-year period. Against this background, semi-structured qualitative interviews were conducted with 30 operators and eight drivers from different parts of the city to explore their aspirations and views on reform. Access was arranged through trusted intermediaries and the eight associations to which respondents belonged. The research revealed that operators were not necessarily passive players waiting for government-led change: some established large transport enterprises, whereas others built small-scale businesses. Propositions were subsequently drawn, amongst other things, on the prospects of and potential revisions to the reform programmes. The recapitalisation programme has had the broader reach of the two programmes. The national government should consider extending it and reviewing its financial support mechanism to make it more accessible to small operators. Larger businesses might be well positioned for incorporation in bus operating companies, but concerted efforts must be made to build trust with these operators and to familiarise them with the transition process. By documenting operator incorporation in the bus system, and providing first-hand insight into paratransit aspirations and attitudes to reform, the research ultimately contributes a basis from which to understand operators' existing responses to reform and the potential for their greater participation in it

Seasons of Hunger: Fighting Cycles of Quiet Starvation Among the World’s Rural Poor

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A Duality Based 2-Approximation Algorithm for Maximum Agreement Forest

We give a 2-approximation algorithm for the Maximum Agreement Forest problem on two rooted binary trees. This NP-hard problem has been studied extensively in the past two decades, since it can be used to compute the rooted Subtree Prune-and-Regraft (rSPR) distance between two phylogenetic trees. Our algorithm is combinatorial and its running time is quadratic in the input size. To prove the approximation guarantee, we construct a feasible dual solution for a novel linear programming formulation. In addition, we show this linear program is stronger than previously known formulations, and we give a compact formulation, showing that it can be solved in polynomial tim

Self-medication in three Orange Free State communities

A study on self-care among whites, blacks and coloureds also focused on different forms of self-medication, including non-compliance. Large differences were found in the self-medication behaviour of the three groups. Different correlates of non-compliance were explored, but selfmedication was not found to be a substitute for formal medical care.S Afr Med J 1993; 83: 345-34