Mimicking Networks and Succinct Representations of Terminal Cuts

Given a large edge-weighted network $G$ with $k$ terminal vertices, we wish to compress it and store, using little memory, the value of the minimum cut (or equivalently, maximum flow) between every bipartition of terminals. One appealing methodology to implement a compression of $G$ is to construct a \emph{mimicking network}: a small network $G'$ with the same $k$ terminals, in which the minimum cut value between every bipartition of terminals is the same as in $G$. This notion was introduced by Hagerup, Katajainen, Nishimura, and Ragde [JCSS '98], who proved that such $G'$ of size at most $2^{2^k}$ always exists. Obviously, by having access to the smaller network $G'$, certain computations involving cuts can be carried out much more efficiently. We provide several new bounds, which together narrow the previously known gap from doubly-exponential to only singly-exponential, both for planar and for general graphs. Our first and main result is that every $k$-terminal planar network admits a mimicking network $G'$ of size $O(k^2 2^{2k})$, which is moreover a minor of $G$. On the other hand, some planar networks $G$ require $|E(G')| \ge \Omega(k^2)$. For general networks, we show that certain bipartite graphs only admit mimicking networks of size $|V(G')| \geq 2^{\Omega(k)}$, and moreover, every data structure that stores the minimum cut value between all bipartitions of the terminals must use $2^{\Omega(k)}$ machine words

ESCAPES - evacuation simulation with children, authorities, parents, emotions, and social comparison

In creating an evacuation simulation for training and planning, realistic agents that reproduce known phenomenon are required. Evacuation simulation in the airport domain requires additional features beyond most simulations, including the unique behaviors of firsttime visitors who have incomplete knowledge of the area and families that do not necessarily adhere to often-assumed pedestrian behaviors. Evacuation simulations not customized for the airport domain do not incorporate the factors important to it, leading to inaccuracies when applied to it. In this paper, we describe ESCAPES, a multiagent evacuation simulation tool that incorporates four key features: (i) different agent types; (ii) emotional interactions; (iii) informational interactions; (iv) behavioral interactions. Our simulator reproduces phenomena observed in existing studies on evacuation scenarios and the features we incorporate substantially impact escape time. We use ESCAPES to model the International Terminal at Los Angeles International Airport (LAX) and receive high praise from security officials