A recent (and also imaginary) poll conducted on a sample size of at least five students revealed some interesting results. When asked to identify the keys to success at Oxford, nearly all the correspondents—apart from the two who collapsed from the stress of even hearing the word ‘succeed’—ranked ‘good grades’ at a paltry sixth position. The answer ‘battlehardened liver’ maintained its monopoly on the first position. This is, of course, unsurprising: apart from rowing, rugby, and rowers complaining about rugby, Oxford’s favourite pastime is drinking. The 139 pubs dotted across the town are a testament to this fact.

So if you’re the type of student who only emerges from the shadows of the Bodleian past sun down, wanting to procrastinate and complain about your impending doom—sorry, deadlines—over a pint or two, look no further.  Here I guide you through how to calculate the most efficient pub crawl route through Oxford, with the help of graph theory.

First, we need to define the nodes or vertices of our graph: the pubs. Using TripAdvisor and cross referencing those results with authorities—*cough* crewdaters *cough*—we find that the best pubs for a pub crawl in Oxford are: The Old Bookbinders Ale House; The White Rabbit; The White Horse; Head of the River; and the Turf Tavern. Collating the distances between all pairs of pubs on the graph, we get Table 1.

In the course of this article, we will refer to the connection between any two nodes—pubs—as an edge. The distance between any two pubs will be called the weight of the edge. Therefore, the weight of the edge between the White Horse and the Turf Tavern is 0.1 miles. Furthermore, a ‘path’ between any two nodes refers not to the physical path between the pubs, but the sequence of intermediate pubs from the pub at the source to the pub at the final destination.

We will also be applying the condition that we will visit each edge and each pub only once, without returning to the source. While this may seem frivolous, it prevents our problem from morphing into the infamous Travelling Salesman Problem, to which there is no efficient solution.

The most obvious, brute-force approach of finding the shortest path through each of these pubs requires checking and comparing all possible routes from start to finish. However, with the use of some assumptions and sophisticated algorithms, we can whittle down these possibilities to just five, in other words a shortest path starting at each node.

To perform this magical reduction in possibilities it would be easiest to first look at a method of tracing a path through a graph known as a ‘breadth first search’. Essentially this involves hitting the nodes adjacent to the starting pub, then the nodes adjacent to these nodes and so on. Dijkstra’s Shortest Path Algorithm does exactly the same, but with an additional distance counter that notes the shortest path to each node in the graph from the source.

While this may reduce the possibilities to just five, Dijkstra’s Algorithm is also a ‘greedy’ algorithm, meaning that it will always choose the next step with greatest immediate benefit and, much like a PPE-ist in an argument, will never backtrack when wrong. Therefore, rather than making progress to the endpoint, it will meander on trying to find the next edge with the shortest weight. Thus, we need to consider an alternate algorithm known as the Floyd-Warshall Algorithm that checks whether a node lies on the shortest path between the source and target and gives the length of this shortest path. We will run this with the small modification that all of the pubs need to be present on this path. We get the results presented in Table 2.

Hence, we see that the shortest pub crawl between the five chosen pubs is of length 1.7 miles. But is it really the most efficient? Through the use of a ‘brute force approach’, we can check that the aforementioned path is, in fact, the most efficient path through all the pubs. Given that the average length of a pub crawl through these pubs is 2.68 miles with a maximum distance of 3.4 miles, we get that the chosen path is 37 per cent shorter than most paths. The downside? How many of us would have the strength or willpower to walk 0.7 miles after having visited four pubs?

The noble sight of the red kite soaring above Oxford’s spires and fields is now commonplace, but these graceful birds of prey have had a troubled past in Great Britain. Despite a golden age in the fifteenth century as valued scavengers keeping city streets clean, they were driven to complete extinction in the nineteenth century in Scotland and Wales following persecution and labelling as vermin. Only the collected and continued effort of environmentalists has reinstated this great bird to British skies. This is one of the success stories in a greater quest to return Britain to its more natural state.

The organisation Rewilding Britain is a group dedicated to just this. Imagine a countryside bursting with life, filled with trees, birdsong, and a plethora of awe-inspiring animals: wolves, bison, elk, and wild boar to name but a few.

It is no secret that our country’s biodiversity is not what it used to be. We’ve lost more of our large mammals than any other European country, bar Ireland. Our expanding towns and cities and wasting of resources have pushed our native species out of their natural environments. Many of these are ‘keystone’ species, occupying the centre of our complex intertwined ecosystems. Like vital pillars supporting the weight of a building, removing these fundamental species destabilises the habitat, threatening its collapse.

One such keystone species at the forefront of Rewilding Britain’s attention is the beaver, not seen in Britain for nearly 500 years until their recent successful reintroduction into Scotland and the trail pair introduced to Devon. This is one of Rewilding Britain’s success stories, but beavers are still a long way from being a common site in our countryside. Much more work is needed.

Beavers fundamentally change the landscape through their construction of river dams, slowing water flow by creating staggered, calm pools. These pools provide ideal habitats for many precious species such as otters, water voles, and birds, by forming a safe haven for their young. What’s more, beavers carry with them great economic benefits. The dams that they build act like massive sponges, holding rain water and releasing it slowly after heavy rain, significantly reducing the risk of flooding. They also create many small reservoirs, preserving water supplies in the dry months and thereby reducing the risk of harmful droughts.

Wolves—another keystone species—used to rule the forest as the top predators historically reigning across the British wildlands. But this wasn’t to last, their reign cut short when they were hunted to extinction in the eighteenth century. Although many purport that their introduction would pose a significant risk to humans, wolves actually tend to stay far away from human activity. The proposed sites of reintroduction in Scotland, despite being very remote, are never far from farmers and their livestock, some of which would inevitably be taken. The issue that must be discussed is whether the health of the ecosystem is worth risking the livelihood of the farmers.

The presence of wolves provides massive benefits to the ecosystem, most obviously through preventing the over-grazing of delicate saplings by keeping herds of wild deer on the move. This allows time for trees to grow where previously only open grassland existed, providing a home for plants, ground living mammals, and a multitude of birds. The presence of trees even reduces flood risk by releasing water after rains much slower than open grassland.

These are just a few of the species which Rewilding Britain are working to return to our pleasant shores. Further plans have been proposed for the return and spread of the lynx, wild boar, bison, and elk, along with numerous birds and fish. For these plans to work they need careful planning and testing, like that occurring with a pair of beavers in Devon, to minimise unanticipated effects, but the possibility of seeing these wonderful creatures throughout the British countryside makes it worth the risk.