Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerabl...
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ISBN:
(纸本)9798350387117;9798350387124
Contemporary accelerator designs exhibit a high degree of spatial localization, wherein two-dimensional physical distance determines communication costs between processing elements. This situation presents considerable algorithmic challenges, particularly when managing sparse data, a pivotal component in progressing data science. The spatial computer model quantifies communication locality by weighting processor communication costs by distance, introducing a term named energy. Moreover, it integrates depth, a widely-utilized metric, to promote high parallelism. We propose and analyze a framework for efficient spatial tree algorithms within the spatial computer model. Our primary method constructs a spatial tree layout that optimizes the locality of the neighbors in the compute grid. This approach thereby enables locality-optimized messaging within the tree. Our layout achieves a polynomial factor improvement in energy compared to utilizing a PRAM approach. Using this layout, we develop energy-efficient treefix sum and lowest common ancestor algorithms, which are both fundamental building blocks for other graph algorithms. With high probability, our algorithms exhibit near-linear energy and poly-logarithmic depth. Our contributions augment a growing body of work demonstrating that computations can have both high spatial locality and low depth. Moreover, our work constitutes an advancement in the spatial layout of irregular and sparse computations.
In this paper, we propose a new problem called the Maximum cardinality Acyclic Subset of Edges that Meets the Potential Requirements (MASEMPR). This problem abstracts several problems in logistics. Our focus is on a p...
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Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived ...
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In recent years, the explosion of big data and analytics has necessitated distributed storage and processing with several compute nodes (e.g., multiple datacenters). These nodes collaboratively perform parallel comput...
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ISBN:
(纸本)9783959773607
In recent years, the explosion of big data and analytics has necessitated distributed storage and processing with several compute nodes (e.g., multiple datacenters). These nodes collaboratively perform parallel computation, where the data is typically partitioned across these nodes to ensure scalability, redundancy and load-balancing. But the nodes may not always be co-located;in many cases, they are part of a larger communication network. Since those nodes only need to communicate among themselves, a key challenge is to design efficient routes catered to that subnetwork. In this work, we initiate the study of distributed sampling and routing problems for subnetworks in any well-connected network. Given any network G = (V,E) with mixing time τmix, consider the canonical problem of permutation routing [Ghaffari, Kuhn and Su, PODC 2017] that aims to minimize both congestion and dilation of the routes, where the demands (i.e., set of source-terminal pairs) are such that each node sends or receives number of messages proportional to its degree. We show that the permutation routing problem, when demands are restricted to any subset S ⊆ V (i.e., subnetwork), can be solved in exp(O(√log |S|)) · Õ(τmix) rounds (where Õ (·) hides polylogarithmic factors of |V |). This means that the running time depends subpolynomially on the subnetwork size (i.e., not on the entire network size). The ability to solve permutation routing efficiently immediately implies that a large class of parallel algorithms can be simulated efficiently on the subnetwork. As a prerequisite to constructing efficient routes, we design and analyze distributed branching random walks that distribute tokens started by the nodes in the subnetwork. At a high-level, these algorithms operate by always moving each token according to a (lazy) simple random walk, but also branching a token into multiple tokens at some specified intervals;ultimately, if a node starts a branching walk, with its id in a token, then by the
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and problem specific queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial tim...
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For an undirected graph G = (V, E), with n vertices and m edges, the densest subgraph problem, is to compute a subset S ⊆ V which maximizes the ratio |ES|/|S|, where ES ⊆ E is the set of all edges of G with endpoints ...
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The palette sparsification theorem (PST) of Assadi, Chen, and Khanna (SODA 2019) states that in every graph G with maximum degree ∆, sampling a list of O(log n) colors from {1, ..., ∆ + 1} for every vertex independent...
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In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed gr...
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ISBN:
(纸本)9798350382853;9798350382846
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically independent, while under the alternative, the edges of one graph are dependent on the edges of a randomly vertex-permuted version of the other graph. For general edge-weights distributions, we establish thresholds at which optimal testing is information-theoretically impossible and possible, as a function of the total number of nodes in the observed graphs and the generative distributions of the weights. Finally, we observe a statistical-computational gap in our problem, and we provide evidence that this is fundamental using the framework of low-degree polynomials.
Basic and applied research have been a pair of popular yet vaguely-defined concepts in scientific philosophy and technology management. This classification gets further challenged as once-theoretical studies like Arti...
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We consider the problem of coloring graphs of maximum degree ∆ with ∆ colors in the distributed setting with limited bandwidth. Specifically, we give a poly log log n-round randomized algorithm in the CONGEST model. T...
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