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1. Local Access to Huge Random Objects through Partial Sampling

   Biswas, Amartya Shankha; Rubinfeld, Ronitt; Yodpinyanee, Anak (January 2020, 11th Innovations in Theoretical Computer Science (ITCS 2020))

   Consider an algorithm performing a computation on a huge random object. Is it necessary to generate the entire object up front, or is it possible to provide query access to the object and sample it incrementally "on-the-fly"? Such an implementation should emulate the object by answering queries in a manner consistent with a random instance sampled from the true distribution. Our first set of results focus on undirected graphs with independent edge probabilities, under certain assumptions. Then, we use this to obtain the first efficient implementations for the Erdos-Renyi model and the Stochastic Block model. As in previous local-access implementations for random graphs, we support Vertex-Pair and Next-Neighbor queries. We also introduce a new Random-Neighbor query. Next, we show how to implement random Catalan objects, specifically focusing on Dyck paths (always positive random walks on the integer line). Here, we support Height queries to find the position of the walk, and First-Return queries to find the time when the walk returns to a specified height. This in turn can be used to implement Next-Neighbor queries on random rooted/binary trees, and Matching-Bracket queries on random well bracketed expressions. Finally, we define a new model that: (1) allows multiple independent simultaneous instantiations of the same implementation to be consistent with each other without communication (2) allows us to generate a richer class of random objects that do not have a succinct description. Specifically, we study uniformly random valid q-colorings of an input graph G with max degree Δ. The distribution over valid colorings is specified via a "huge" underlying graph G, that is far too large to be read in sub-linear time. Instead, we access G through local neighborhood probes. We are able to answer queries to the color of any vertex in sub-linear time for q>9Δ. 

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2. Dwell Regions: Generalized Stay Regions For Streaming and Archival Trajectory Data

   https://doi.org/10.1145/3543850  

   Uddin, Reaz; Mahin, Mehnaz Tabassum; Rajan, Payas; Ravishankar, Chinya V.; Tsotras, Vassilis J. (January 2022, ACM Transactions on Spatial Algorithms and Systems)

   A region \(\mathcal {R} \) is a dwell region for a moving object O if, given a threshold distance r q and duration τ q , every point of \(\mathcal {R} \) remains within distance r q from O for at least time τ q . Points within \(\mathcal {R} \) are likely to be of interest to O , so identification of dwell regions has applications such as monitoring and surveillance. We first present a logarithmic-time online algorithm to find dwell regions in an incoming stream of object positions. Our method maintains the upper and lower bounds for the radius of the smallest circle enclosing the object positions, thereby greatly reducing the number of trajectory points needed to evaluate the query. It approximates the radius of the smallest circle enclosing a given subtrajectory within an arbitrarily small user-defined factor, and is also able to efficiently answer decision queries asking whether or not a dwell region exists. For the offline version of the dwell region problem, we first extend our online approach to develop the ρ -Index, which indexes subtrajectories using query radius ranges. We then refine this approach to obtain the τ -Index, which indexes subtrajectories using both query radius ranges and dwell durations. Our experiments using both real-world and synthetic datasets show that the online approach can scale up to hundreds of thousands of moving objects. For archived trajectories, our indexing approaches speed up queries by many orders of magnitude. 

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3. CaSPR: Learning Canonical Spatiotemporal Point Cloud Representations

   Rempe, Davis; Birdal, Tolga; Zhao, Yongheng; Gojcic, Zan; Sridhar, Srinath; Guibas, Leonidas (January 2020, Advances in neural information processing systems)

   null (Ed.)

   We propose CaSPR, a method to learn object-centric Canonical Spatiotemporal Point Cloud Representations of dynamically moving or evolving objects. Our goal is to enable information aggregation over time and the interrogation of object state at any spatiotemporal neighborhood in the past, observed or not. Different from previous work, CaSPR learns representations that support spacetime continuity, are robust to variable and irregularly spacetime-sampled point clouds, and generalize to unseen object instances. Our approach divides the problem into two subtasks. First, we explicitly encode time by mapping an input point cloud sequence to a spatiotemporally-canonicalized object space. We then leverage this canonicalization to learn a spatiotemporal latent representation using neural ordinary differential equations and a generative model of dynamically evolving shapes using continuous normalizing flows. We demonstrate the effectiveness of our method on several applications including shape reconstruction, camera pose estimation, continuous spatiotemporal sequence reconstruction, and correspondence estimation from irregularly or intermittently sampled observations. 

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4. Local Access to Huge Random Objects Through Partial Sampling

   Biswas, Amartya Shankha; Rubinfeld, Ronitt; Yodpinyanee, Anak (January 2020, 11th Innovations in Theoretical Computer Science Conference, ITCS 2020)

   null (Ed.)

   Consider an algorithm performing a computation on a huge random object (for example a random graph or a "long" random walk). Is it necessary to generate the entire object prior to the computation, or is it possible to provide query access to the object and sample it incrementally "on-the-fly" (as requested by the algorithm)? Such an implementation should emulate the random object by answering queries in a manner consistent with an instance of the random object sampled from the true distribution (or close to it). This paradigm is useful when the algorithm is sub-linear and thus, sampling the entire object up front would ruin its efficiency. Our first set of results focus on undirected graphs with independent edge probabilities, i.e. each edge is chosen as an independent Bernoulli random variable. We provide a general implementation for this model under certain assumptions. Then, we use this to obtain the first efficient local implementations for the Erdös-Rényi G(n,p) model for all values of p, and the Stochastic Block model. As in previous local-access implementations for random graphs, we support Vertex-Pair and Next-Neighbor queries. In addition, we introduce a new Random-Neighbor query. Next, we give the first local-access implementation for All-Neighbors queries in the (sparse and directed) Kleinberg’s Small-World model. Our implementations require no pre-processing time, and answer each query using O(poly(log n)) time, random bits, and additional space. Next, we show how to implement random Catalan objects, specifically focusing on Dyck paths (balanced random walks on the integer line that are always non-negative). Here, we support Height queries to find the location of the walk, and First-Return queries to find the time when the walk returns to a specified location. This in turn can be used to implement Next-Neighbor queries on random rooted ordered trees, and Matching-Bracket queries on random well bracketed expressions (the Dyck language). Finally, we introduce two features to define a new model that: (1) allows multiple independent (and even simultaneous) instantiations of the same implementation, to be consistent with each other without the need for communication, (2) allows us to generate a richer class of random objects that do not have a succinct description. Specifically, we study uniformly random valid q-colorings of an input graph G with maximum degree Δ. This is in contrast to prior work in the area, where the relevant random objects are defined as a distribution with O(1) parameters (for example, n and p in the G(n,p) model). The distribution over valid colorings is instead specified via a "huge" input (the underlying graph G), that is far too large to be read by a sub-linear time algorithm. Instead, our implementation accesses G through local neighborhood probes, and is able to answer queries to the color of any given vertex in sub-linear time for q ≥ 9Δ, in a manner that is consistent with a specific random valid coloring of G. Furthermore, the implementation is memory-less, and can maintain consistency with non-communicating copies of itself. 

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5. Efficient algorithms for dynamic bidirected Dyck-reachability

   https://doi.org/10.1145/3498724  

   Li, Yuanbo; Satya, Kris; Zhang, Qirun (January 2022, Proceedings of the ACM on Programming Languages)

   Dyck-reachability is a fundamental formulation for program analysis, which has been widely used to capture properly-matched-parenthesis program properties such as function calls/returns and field writes/reads. Bidirected Dyck-reachability is a relaxation of Dyck-reachability on bidirected graphs where each edge u → ( i v labeled by an open parenthesis “( i ” is accompanied with an inverse edge v → ) i u labeled by the corresponding close parenthesis “) i ”, and vice versa. In practice, many client analyses such as alias analysis adopt the bidirected Dyck-reachability formulation. Bidirected Dyck-reachability admits an optimal reachability algorithm. Specifically, given a graph with n nodes and m edges, the optimal bidirected Dyck-reachability algorithm computes all-pairs reachability information in O ( m ) time. This paper focuses on the dynamic version of bidirected Dyck-reachability. In particular, we consider the problem of maintaining all-pairs Dyck-reachability information in bidirected graphs under a sequence of edge insertions and deletions. Dynamic bidirected Dyck-reachability can formulate many program analysis problems in the presence of code changes. Unfortunately, solving dynamic graph reachability problems is challenging. For example, even for maintaining transitive closure, the fastest deterministic dynamic algorithm requires O ( n 2 ) update time to achieve O (1) query time. All-pairs Dyck-reachability is a generalization of transitive closure. Despite extensive research on incremental computation, there is no algorithmic development on dynamic graph algorithms for program analysis with worst-case guarantees. Our work fills the gap and proposes the first dynamic algorithm for Dyck reachability on bidirected graphs. Our dynamic algorithms can handle each graph update ( i.e. , edge insertion and deletion) in O ( n ·α( n )) time and support any all-pairs reachability query in O (1) time, where α( n ) is the inverse Ackermann function. We have implemented and evaluated our dynamic algorithm on an alias analysis and a context-sensitive data-dependence analysis for Java. We compare our dynamic algorithms against a straightforward approach based on the O ( m )-time optimal bidirected Dyck-reachability algorithm and a recent incremental Datalog solver. Experimental results show that our algorithm achieves orders of magnitude speedup over both approaches. 

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