Deterministic Graph Exploration with Advice

We consider the task of graph exploration. An $n$-node graph has unlabeled nodes, and all ports at any node of degree $d$ are arbitrarily numbered $0,\dots, d-1$. A mobile agent has to visit all nodes and stop. The exploration time is the number of edge traversals. We consider the problem of how much knowledge the agent has to have a priori, in order to explore the graph in a given time, using a deterministic algorithm. This a priori information (advice) is provided to the agent by an oracle, in the form of a binary string, whose length is called the size of advice. We consider two types of oracles. The instance oracle knows the entire instance of the exploration problem, i.e., the port-numbered map of the graph and the starting node of the agent in this map. The map oracle knows the port-numbered map of the graph but does not know the starting node of the agent. We first consider exploration in polynomial time, and determine the exact minimum size of advice to achieve it. This size is $\log\log\log n -\Theta(1)$, for both types of oracles. When advice is large, there are two natural time thresholds: $\Theta(n^2)$ for a map oracle, and $\Theta(n)$ for an instance oracle, that can be achieved with sufficiently large advice. We show that, with a map oracle, time $\Theta(n^2)$ cannot be improved in general, regardless of the size of advice. We also show that the smallest size of advice to achieve this time is larger than $n^\delta$, for any $\delta <1/3$. For an instance oracle, advice of size $O(n\log n)$ is enough to achieve time $O(n)$. We show that, with any advice of size $o(n\log n)$, the time of exploration must be at least $n^\epsilon$, for any $\epsilon <2$, and with any advice of size $O(n)$, the time must be $\Omega(n^2)$. We also investigate minimum advice sufficient for fast exploration of hamiltonian graphs

Topology recognition with advice

In topology recognition, each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph, with all ports correctly marked. This task is usually unfeasible without any a priori information. Such information can be provided to nodes as advice. An oracle knowing the network can give a (possibly different) string of bits to each node, and all nodes must reconstruct the network using this advice, after a given number of rounds of communication. During each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations. The time of completing topology recognition is the number of rounds it takes, and the size of advice is the maximum length of a string given to nodes. We investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes. We provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time, in the class of all graphs of size $n$ and diameter $D\le \alpha n$, for any constant $\alpha< 1$. In most cases, our bounds are asymptotically tight

Understanding farmers’ indicators in climate-smart agriculture prioritization in the Southern Agricultural Growth Corridor of Tanzania (SAGCOT).

In order to increase the uptake of climate-smart agriculture (CSA) technologies, it is important to understand the contexts in which farmers operate. Farmers use different indicators to decide whether or not to implement, what to implement, and where to implement specific technologies. Identifying and understanding such indicators can be helpful to efforts aiming to scale out adoption. The purpose of this study was to identify indicators that farmers use to prioritize agricultural innovations, in general, and CSA, in particular. Kilolo and Mbarali Districts lie in the Southern Agricultural Growth Corridor of Tanzania. Four participatory workshops, in the form of focus group discussions, were conducted in these two districts. In each district, a separate workshop was held with farmers from each agro-ecological zone (AEZ). Separate workshops were held with farmers and experts to explore differences between stakeholders and across the districts regarding perceptions of the status of soil fertility, prioritized practices, and ranking of indicators for prioritizing practices. Characterization of the AEZ, prioritization of practices, identification of indicators for prioritizing CSA, and selection of practices for demonstration as well as sites for the demonstration plots were done separately with men and women groups. Practices were prioritized using pairwise ranking, while indicators were scored on a rating scale from least important (1) to most important (5). Results showed that, both in Kilolo and Mbarali Districts, farmers perceive the status of soil fertility as poor. Up to 60 % of the workshop participants were not satisfied with the status of soil fertility in their farms. More than 80% of workshop participants in each of the four workshops reported that they practiced burning. The main reasons for burning were to save labour and time and to reduce crop–livestock conflict. The men’s group in the upland zone in Mbarali District ranked mulching, water harvesting, improved varieties, and crop rotation as the most important practices in respective order. In the lowlands, both men and women groups selected irrigation, chemical fertilizer, and crop rotation as most relevant practices. Awareness and use of the practices was low among participants in the two workshops. The most prioritized practices by the women’s group in the uplands, Kilolo District, were improved breeds and improved varieties. Intercropping was the least prioritized practice. The men’s group prioritized improved varieties and pesticides application, while irrigation and fertilizer application ranked lowest. In the lowlands, men’s and women’s groups prioritized irrigation, inorganic fertilizer and improved varieties as most important. Mulching and herbicides ranked as least prioritized. In addition, the men’s group from the lowland zone ranked pesticide application among the most important practices, while farmyard manure and zero grazing were ranked as least important. Important indicators that farmers identified to prioritize agricultural practices across the two districts included yield, income, cost, labour, availability of inputs, the status of soil fertility, and knowledge about the practices. Several practices were selected for the proposed CSA demonstration plots. The women’s group in the uplands zone in Mbarali prioritized improved crop varieties, water harvesting, mulching, and fertilizer application. The men’s group chose irrigation, herbicides, inorganic fertilizers, and seed selection. In the lowlands, improved crop varieties, inorganic fertilizer, farmyard manure, and mulching were selected by women. Men preferred seed preparation, right use of fertilizers (i.e., rate and type), integrated pest management, and improved storage. The selected important practices for demonstration in the uplands in Kilolo District were minimum tillage, soil testing, improved varieties, fertilizer application, and irrigation. Farmers in the lowlands chose production of clean seeds of different crops, such as tomatoes, beans, maize, and chillies. In addition, they were interested in learning about fertilizer application, pesticides application, and preparation and application of compost manure. The findings of this research have several implications for policy. First, there is need to increase awareness of farmers about CSA practices, particularly those that they prioritize. The finding that farmers perceive poor soil fertility but do not prioritize soil fertility management practices implies the need to promote adoption of such technologies. Thirdly, a bottom-up approach that involves working with farmers to prioritize agricultural practices suitable for their specific AEZ and preferred by either the men or women is important to inform investment of limited resources to increase food security and resilience to climate risks while minimizing trade-offs. The findings highlight indicators that influence farmers’ adoption of agricultural practices as well as constraints to implementation

Business networks SMEs and inter-firm collaboration: a review of the research literature with implications for policy

This literature review, which was commissioned by the UK's Small Business Service is concerned with business networks, and their importance for the small business community. Business networks are sometimes defined as comprising only inter-firm relationships (e.g. those that exist between component supplier and a manufacturer). However, it soon becomes apparent that a broader perspective is required, if research findings are to contribute meaningful insights for policy and practice. We have therefore incorporated research evidence on personal networks, notably those associated with entrepreneurship, and on links between firms and supporting institutions, such as trade associations, government agencies and universities

Time vs. Information Tradeoffs for Leader Election in Anonymous Trees

The leader election task calls for all nodes of a network to agree on a single node. If the nodes of the network are anonymous, the task of leader election is formulated as follows: every node $v$ of the network must output a simple path, coded as a sequence of port numbers, such that all these paths end at a common node, the leader. In this paper, we study deterministic leader election in anonymous trees. Our aim is to establish tradeoffs between the allocated time $\tau$ and the amount of information that has to be given $\textit{a priori}$ to the nodes to enable leader election in time $\tau$ in all trees for which leader election in this time is at all possible. Following the framework of $\textit{algorithms with advice}$, this information (a single binary string) is provided to all nodes at the start by an oracle knowing the entire tree. The length of this string is called the $\textit{size of advice}$. For an allocated time $\tau$, we give upper and lower bounds on the minimum size of advice sufficient to perform leader election in time $\tau$. We consider $n$-node trees of diameter $diam \leq D$. While leader election in time $diam$ can be performed without any advice, for time $diam-1$ we give tight upper and lower bounds of $\Theta (\log D)$. For time $diam-2$ we give tight upper and lower bounds of $\Theta (\log D)$ for even values of $diam$, and tight upper and lower bounds of $\Theta (\log n)$ for odd values of $diam$. For the time interval $[\beta \cdot diam, diam-3]$ for constant $\beta >1/2$, we prove an upper bound of $O(\frac{n\log n}{D})$ and a lower bound of $\Omega(\frac{n}{D})$, the latter being valid whenever $diam$ is odd or when the time is at most $diam-4$. Finally, for time $\alpha \cdot diam$ for any constant $\alpha <1/2$ (except for the case of very small diameters), we give tight upper and lower bounds of $\Theta (n)$