Almost Linear Time Algorithms for Some Problems on Dynamic Flow Networks

Motivated by evacuation planning, several problems regarding dynamic flow networks have been studied in recent years. A dynamic flow network consists of an undirected graph with positive edge lengths, positive edge capacities, and positive vertex weights. The road network in an area can be treated as a graph where the edge lengths are the distances along the roads and the vertex weights are the number of people at each site. An edge capacity limits the number of people that can enter the edge per unit time. In a dynamic flow network, when particular points on edges or vertices called sinks are given, all of the people are required to evacuate from the vertices to the sinks as quickly as possible. This chapter gives an overview of two of our recent results on the problem of locating multiple sinks in a dynamic flow path network such that the max/sum of evacuation times for all the people to sinks is minimized, and we focus on techniques that enable the problems to be solved in almost linear time.

The Steiner cycle and path cover problem on interval graphs

The Steiner path problem is a common generalization of the Steiner tree and the Hamiltonian path problem, in which we have to decide if for a given graph there exists a path visiting a fixed set of terminals. In the Steiner cycle problem we look for a cycle visiting all terminals instead of a path. The Steiner path cover problem is an optimization variant of the Steiner path problem generalizing the path cover problem, in which one has to cover all terminals with a minimum number of paths. We study those problems for the special class of interval graphs. We present linear time algorithms for both the Steiner path cover problem and the Steiner cycle problem on interval graphs given as endpoint sorted lists. The main contribution is a lemma showing that backward steps to non-Steiner intervals are never necessary. Furthermore, we show how to integrate this modification to the deferred-query technique of Chang et al. to obtain the linear running times.

Reversed Lempel–Ziv Factorization with Suffix Trees

We present linear-time algorithms computing the reversed Lempel–Ziv factorization [Kolpakov and Kucherov, TCS’09] within the space bounds of two different suffix tree representations. We can adapt these algorithms to compute the longest previous non-overlapping reverse factor table [Crochemore et al., JDA’12] within the same space but pay a multiplicative logarithmic time penalty.

Constructing smaller genome graphs via string compression

The size of a genome graph — the space required to store the nodes, their labels and edges — affects the efficiency of operations performed on it. For example, the time complexity to align a sequence to a graph without a graph index depends on the total number of characters in the node labels and the number of edges in the graph. The size of the graph also affects the size of the graph index that is used to speed up the alignment. This raises the need for approaches to construct space-efficient genome graphs.We point out similarities in the string encoding approaches of genome graphs and the external pointer macro (EPM) compression model. Supported by these similarities, we present a pair of linear-time algorithms that transform between genome graphs and EPM-compressed forms. We show that the algorithms result in an upper bound on the size of the genome graph constructed based on an optimal EPM compression. In addition to the transformation, we show that equivalent choices made by EPM compression algorithms may result in different sizes of genome graphs. To further optimize the size of the genome graph, we purpose the source assignment problem that optimizes over the equivalent choices during compression and introduce an ILP formulation that solves that problem optimally. As a proof-of-concept, we introduce RLZ-Graph, a genome graph constructed based on the relative Lempel-Ziv EPM compression algorithm. We show that using RLZ-Graph, across all human chromosomes, we are able to reduce the disk space to store a genome graph on average by 40.7% compared to colored de Bruijn graphs constructed by Bifrost under the default settings.The RLZ-Graph software is available at https://github.com/Kingsford-Group/rlzgraph

Working Set Analytics

The working set model for program behavior was invented in 1965. It has stood the test of time in virtual memory management for over 50 years. It is considered the ideal for managing memory in operating systems and caches. Its superior performance was based on the principle of locality, which was discovered at the same time; locality is the observed tendency of programs to use distinct subsets of their pages over extended periods of time. This tutorial traces the development of working set theory from its origins to the present day. We will discuss the principle of locality and its experimental verification. We will show why working set memory management resists thrashing and generates near-optimal system throughput. We will present the powerful, linear-time algorithms for computing working set statistics and applying them to the design of memory systems. We will debunk several myths about locality and the performance of memory systems. We will conclude with a discussion of the application of the working set model in parallel systems, modern shared CPU caches, network edge caches, and inventory and logistics management.

Learning DOM Trees of Web Pages by Subpath Kernel and Detecting Fake e-Commerce Sites

The subpath kernel is a class of positive definite kernels defined over trees, which has the following advantages for the purposes of classification, regression and clustering: it can be incorporated into a variety of powerful kernel machines including SVM; It is invariant whether input trees are ordered or unordered; It can be computed by significantly fast linear-time algorithms; And, finally, its excellent learning performance has been proven through intensive experiments in the literature. In this paper, we leverage recent advances in tree kernels to solve real problems. As an example, we apply our method to the problem of detecting fake e-commerce sites. Although the problem is similar to phishing site detection, the fact that mimicking existing authentic sites is harmful for fake e-commerce sites marks a clear difference between these two problems. We focus on fake e-commerce site detection for three reasons: e-commerce fraud is a real problem that companies and law enforcement have been cooperating to solve; Inefficiency hampers existing approaches because datasets tend to be large, while subpath kernel learning overcomes these performance challenges; And we offer increased resiliency against attempts to subvert existing detection methods through incorporating robust features that adversaries cannot change: the DOM-trees of web-sites. Our real-world results are remarkable: our method has exhibited accuracy as high as 0.998 when training SVM with 1000 instances and evaluating accuracy for almost 7000 independent instances. Its generalization efficiency is also excellent: with only 100 training instances, the accuracy score reached 0.996.