The detour order of a graph G, denoted by τ (G) , is the order of a longest path in G. A partition of the vertex set of G into two sets, A and B, such that τ(〈A〉) ≤ a and τ(〈B〉) ≤ b is called an (a, b)-partition of G. If G has an (a, b)-partition for every pair (a, b) of positive integers such that a + b = τ(G), then we say that G is τ -partitionable. The Path Partition Conjecture (PPC), which ...

To successfully realize the ubiquitous network environment including home automation or industrial control systems, it is important to be able to resist a jamming attack. This has recently been considered as an extremely threatening attack because it can collapse the entire network, despite the existence of basic security protocols such as encryption and authentication. In this paper, we presen...

Long network latency negatively impacts the performance of online multiplayer games. In this thesis, we propose a novel approach to reduce the network latency in online gaming. Our approach employs application level detour routing in which game-state update messages between two players can be forwarded through other intermediate relay nodes in order to reduce network latency. We present results...

We studied detour responses of two species of poeciliid fish (Gambusia hoolbroki and Girardinus falcatus) faced with a vertical-bar barrier, through which conspecifics of the same or different sex or a simulated-predator (which induced detour behaviour for predator-inspection responses) were visible. Both species showed a consistent bias to turn leftward when faced with the predator, and a cons...

Let G be an embedded planar graph whose edges are curves. The detour between two points p and q (on edges or vertices) of G is the length of a shortest path connecting p and q in G divided by their Euclidean distance |pq|. The maximum detour over all pairs of points is called the geometric dilation δ(G). EbbersBaumann, Grüne and Klein have shown that every finite point set is contained in a pla...

Topological phase transition is accompanied with a change of topological numbers. According to the bulk-edge correspondence, the gap closing and the breakdown of the adiabaticity are necessary at the phase transition point to make the topological number ill-defined. However, the gap closing is not always needed. In this paper, we show that two topological distinct phases can be continuously con...