Optimal path planning for surveillance with temporal-logic constraints

In this paper we present a method for automatically generating optimal robot paths satisfying high-level mission specifications. The motion of the robot in the environment is modeled as a weighted transition system. The mission is specified by an arbitrary linear temporal-logic (LTL) formula over propositions satisfied at the regions of a partitioned environment. The mission specification contains an optimizing proposition, which must be repeatedly satisfied. The cost function that we seek to minimize is the maximum time between satisfying instances of the optimizing proposition. For every environment model, and for every formula, our method computes a robot path that minimizes the cost function. The problem is motivated by applications in robotic monitoring and data-gathering. In this setting, the optimizing proposition is satisfied at all locations where data can be uploaded, and the LTL formula specifies a complex data-collection mission. Our method utilizes Büchi automata to produce an automaton (which can be thought of as a graph) whose runs satisfy the temporal-logic specification. We then present a graph algorithm that computes a run corresponding to the optimal robot path. We present an implementation for a robot performing data collection in a road-network platform.This material is based upon work supported in part by ONR-MURI (award N00014-09-1-1051), ARO (award W911NF-09-1-0088), and Masaryk University (grant numbers LH11065 and GD102/09/H042), and other funding sources (AFOSR YIP FA9550-09-1-0209, NSF CNS-1035588, NSF CNS-0834260). (N00014-09-1-1051 - ONR-MURI; W911NF-09-1-0088 - ARO; LH11065 - Masaryk University; GD102/09/H042 - Masaryk University; FA9550-09-1-0209 - AFOSR YIP; CNS-1035588 - NSF; CNS-0834260 - NSF

Hierarchical Time-Dependent Oracles

We study networks obeying \emph{time-dependent} min-cost path metrics, and present novel oracles for them which \emph{provably} achieve two unique features: % (i) \emph{subquadratic} preprocessing time and space, \emph{independent} of the metric's amount of disconcavity; % (ii) \emph{sublinear} query time, in either the network size or the actual Dijkstra-Rank of the query at hand

Exact Ground States of Large Two-Dimensional Planar Ising Spin Glasses

Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 3000x3000 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the Bieche et al. approach.Comment: 11 pages, 5 figures; shortened introduction, extended results; to appear in Physical Review E 7

Typical and large-deviation properties of minimum-energy paths on disordered hierarchical lattices

We perform numerical simulations to study the optimal path problem on disordered hierarchical graphs with effective dimension d=2.32. Therein, edge energies are drawn from a disorder distribution that allows for positive and negative energies. This induces a behavior which is fundamentally different from the case where all energies are positive, only. Upon changing the subtleties of the distribution, the scaling of the minimum energy path length exhibits a transition from self-affine to self-similar. We analyze the precise scaling of the path length and the associated ground-state energy fluctuations in the vincinity of the disorder critical point, using a decimation procedure for huge graphs. Further, using an importance sampling procedure in the disorder we compute the negative-energy tails of the ground-state energy distribution up to 12 standard deviations away from its mean. We find that the asymptotic behavior of the negative-energy tail is in agreement with a Tracy-Widom distribution. Further, the characteristic scaling of the tail can be related to the ground-state energy flucutations, similar as for the directed polymer in a random medium.Comment: 10 pages, 10 figures, 3 table

A Selectivity based approach to Continuous Pattern Detection in Streaming Graphs

Cyber security is one of the most significant technical challenges in current times. Detecting adversarial activities, prevention of theft of intellectual properties and customer data is a high priority for corporations and government agencies around the world. Cyber defenders need to analyze massive-scale, high-resolution network flows to identify, categorize, and mitigate attacks involving networks spanning institutional and national boundaries. Many of the cyber attacks can be described as subgraph patterns, with prominent examples being insider infiltrations (path queries), denial of service (parallel paths) and malicious spreads (tree queries). This motivates us to explore subgraph matching on streaming graphs in a continuous setting. The novelty of our work lies in using the subgraph distributional statistics collected from the streaming graph to determine the query processing strategy. We introduce a "Lazy Search" algorithm where the search strategy is decided on a vertex-to-vertex basis depending on the likelihood of a match in the vertex neighborhood. We also propose a metric named "Relative Selectivity" that is used to select between different query processing strategies. Our experiments performed on real online news, network traffic stream and a synthetic social network benchmark demonstrate 10-100x speedups over selectivity agnostic approaches.Comment: in 18th International Conference on Extending Database Technology (EDBT) (2015