/pdf/scalable-molecular-dynamics-with-namd-3j7xyc70g4.pdf

Scalable Molecular Dynamics with NAMD

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

The mapping of large-scale human movements is important for urban planning, traffic forecasting and epidemic prevention. Work in animals had suggested that their foraging might be explained in terms of a random walk, a mathematical rendition of a series of random steps, or a Levy flight, a random walk punctuated by occasional larger steps. The role of Levy statistics in animal behaviour is much debated — as explained in an accompanying News Feature — but the idea of extending it to human behaviour was boosted by a report in 2006 of Levy flight-like patterns in human movement tracked via dollar bills. A new human study, based on tracking the trajectory of 100,000 cell-phone users for six months, reveals behaviour close to a Levy pattern, but deviating from it as individual trajectories show a high degree of temporal and spatial regularity: work and other commitments mean we are not as free to roam as a foraging animal. But by correcting the data to accommodate individual variation, simple and predictable patterns in human travel begin to emerge. The cover photo (by Cesar Hidalgo) captures human mobility in New York's Grand Central Station. This study used a sample of 100,000 mobile phone users whose trajectory was tracked for six months to study human mobility patterns. Displacements across all users suggest behaviour close to the Levy-flight-like pattern observed previously based on the motion of marked dollar bills, but with a cutoff in the distribution. The origin of the Levy patterns observed in the aggregate data appears to be population heterogeneity and not Levy patterns at the level of the individual. Despite their importance for urban planning1, traffic forecasting2 and the spread of biological3,4,5 and mobile viruses6, our understanding of the basic laws governing human motion remains limited owing to the lack of tools to monitor the time-resolved location of individuals. Here we study the trajectory of 100,000 anonymized mobile phone users whose position is tracked for a six-month period. We find that, in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models7, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time-independent characteristic travel distance and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that, despite the diversity of their travel history, humans follow simple reproducible patterns. This inherent similarity in travel patterns could impact all phenomena driven by human mobility, from epidemic prevention to emergency response, urban planning and agent-based modelling.

/pdf/understanding-individual-human-mobility-patterns-3k1tyob274.pdf

Understanding individual human mobility patterns

We present Tor, a circuit-based low-latency anonymous communication service. This second-generation Onion Routing system addresses limitations in the original design by adding perfect forward secrecy, congestion control, directory servers, integrity checking, configurable exit policies, and a practical design for location-hidden services via rendezvous points. Tor works on the real-world Internet, requires no special privileges or kernel modifications, requires little synchronization or coordination between nodes, and provides a reasonable tradeoff between anonymity, usability, and efficiency. We briefly describe our experiences with an international network of more than 30 nodes. We close with a list of open problems in anonymous communication.

/pdf/tor-the-second-generation-onion-router-2qfrg0ppqb.pdf

Tor: the second-generation onion router

NetworkX is a Python language package for exploration and analysis of networks and network algorithms. The core package provides data structures for representing many types of networks, or graphs, including simple graphs, directed graphs, and graphs with parallel edges and self-loops. The nodes in NetworkX graphs can be any (hashable) Python object and edges can contain arbitrary data; this flexibility makes NetworkX ideal for representing networks found in many dierent scientific fields. In addition to the basic data structures many graph algorithms are implemented for calculating network properties and structure measures: shortest paths, betweenness centrality, clustering, and degree distribution and many more. NetworkX can read and write various graph formats for easy exchange with existing data, and provides generators for many classic graphs and popular graph models, such as the Erdos-Renyi, Small World, and Barabasi-Albert models. The ease-of-use and flexibility of the Python programming language together with connection to the SciPy tools make NetworkX a powerful tool for scientific computations. We discuss some of our recent work studying synchronization of coupled oscillators to demonstrate how NetworkX enables research in the field of computational networks.

/pdf/exploring-network-structure-dynamics-and-function-using-2isdfk9y1h.pdf

Exploring Network Structure, Dynamics, and Function using NetworkX

Moser and Tardos have developed a powerful algorithmic approach (henceforth MT) to the Lovasz Local Lemma (LLL); the basic operation done in MT and its variants is a search for “bad” events in a current configuration. In the initial stage of MT, the variables are set independently. We examine the distributions on these variables that arise during intermediate stages of MT. We show that these configurations have a more or less “random” form, building further on the MT-distribution concept of Haeupler et al. in understanding the (intermediate and) output distribution of MT. This has a variety of algorithmic applications; the most important is that bad events can be found relatively quickly, improving on MT across the complexity spectrum. It makes some polynomial-time algorithms sublinear (e.g., for Latin transversals, which are of basic combinatorial interest), gives lower-degree polynomial runtimes in some settings, transforms certain superpolynomial-time algorithms into polynomial-time algorithms, and leads to Las Vegas algorithms for some coloring problems for which only Monte Carlo algorithms were known.We show that, in certain conditions when the LLL condition is violated, a variant of the MT algorithm can still produce a distribution that avoids most of the bad events. We show in some cases that this MT variant can run faster than the original MT algorithm itself and develop the first-known criterion for the case of the asymmetric LLL. This can be used to find partial Latin transversals—improving on earlier bounds of Stein (1975)—among other applications. We furthermore give applications in enumeration, showing that most applications (for which we aim for all or most of the bad events to be avoided) have large solution sets. We do this by showing that the MT distribution has large Renyi entropy.

https://dl.acm.org/doi/pdf/10.1145/3039869

Algorithmic and Enumerative Aspects of the Moser-Tardos Distribution

We present polylogarithmic approximations for the R|prec|Cmax and R|prec|∑jwjCj problems, when the precedence constraints are “treelike” – i.e., when the undirected graph underlying the precedences is a forest. We also obtain improved bounds for the weighted completion time and flow time for the case of chains with restricted assignment – this generalizes the job shop problem to these objective functions. We use the same lower bound of “congestion+dilation”, as in other job shop scheduling approaches. The first step in our algorithm for the R|prec|Cmax problem with treelike precedences involves using the algorithm of Lenstra, Shmoys and Tardos to obtain a processor assignment with the congestion + dilation value within a constant factor of the optimal. We then show how to generalize the random delays technique of Leighton, Maggs and Rao to the case of trees. For the weighted completion time, we show a certain type of reduction to the makespan problem, which dovetails well with the lower bound we employ for the makespan problem. For the special case of chains, we show a dependent rounding technique which leads to improved bounds on the weighted completion time and new bicriteria bounds for the flow time.

/pdf/scheduling-on-unrelated-machines-under-tree-like-precedence-1khrj5ruek.pdf

Scheduling on unrelated machines under tree-like precedence constraints

On the approximability of clique and related maximization problems

In bipartite matching problems, vertices on one side of a bipartite graph are paired with those on the other. In its online variant, one side of the graph is available offline, while the vertices on the other side arrive online. When a vertex arrives, an irrevocable and immediate decision should be made by the algorithm; either match it to an available vertex or drop it. Examples of such problems include matching workers to firms, advertisers to keywords, organs to patients, and so on. Much of the literature focuses on maximizing the total relevance—modeled via total weight—of the matching. However, in many real-world problems, it is also important to consider contributions of diversity: hiring a diverse pool of candidates, displaying a relevant but diverse set of ads, and so on. In this paper, we propose the Online Submodular Bipartite Matching (OSBM) problem, where the goal is to maximize a submodular function f over the set of matched edges. This objective is general enough to capture the notion of both diversity (e.g., a weighted coverage function) and relevance (e.g., the traditional linear function)—as well as many other natural objective functions occurring in practice (e.g., limited total budget in advertising settings). We propose novel algorithms that have provable guarantees and are essentially optimal when restricted to various special cases. We also run experiments on real-world and synthetic datasets to validate our algorithms.

/pdf/balancing-relevance-and-diversity-in-online-bipartite-so6ltagot5.pdf

Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity.

We present an approach for efficient design of a signaling network for a network of software switches supporting Internet telephony. While one may take an integer programming approach to solve this problem, it quickly becomes intractable even for modest-sized networks. Instead, our topology design uses random graphs that we show to be nearly optimal in cost, highly connected, and computationally efficient even for large networks. We then formulate a quadratic assignment problem (QAP) to map the abstract topology into the physical network to achieve optimal load balancing for given demand forecasts, which we solve using randomized heuristics. Numerical results on several example networks illustrate the performance and computational efficiency of our method. A graphical design tool has been developed based on our algorithms.

Aravind Srinivasan

Papers

Algorithmic and Enumerative Aspects of the Moser-Tardos Distribution

Scheduling on unrelated machines under tree-like precedence constraints

On the approximability of clique and related maximization problems

Balancing Relevance and Diversity in Online Bipartite Matching via Submodularity.

Optimal design of signaling networks for Internet telephony