The Complexity of Node Blocking for Dags

We consider the following modification of annihilation game called node blocking. Given a directed graph, each vertex can be occupied by at most one token. There are two types of tokens, each player can move his type of tokens. The players alternate their moves and the current player $i$ selects one token of type $i$ and moves the token along a directed edge to an unoccupied vertex. If a player cannot make a move then he loses. We consider the problem of determining the complexity of the game: given an arbitrary configuration of tokens in a directed acyclic graph, does the current player has a winning strategy? We prove that the problem is PSPACE-complete.Comment: 7 pages, 3 figure

Interpreting and using CPDAGs with background knowledge

We develop terminology and methods for working with maximally oriented partially directed acyclic graphs (maximal PDAGs). Maximal PDAGs arise from imposing restrictions on a Markov equivalence class of directed acyclic graphs, or equivalently on its graphical representation as a completed partially directed acyclic graph (CPDAG), for example when adding background knowledge about certain edge orientations. Although maximal PDAGs often arise in practice, causal methods have been mostly developed for CPDAGs. In this paper, we extend such methodology to maximal PDAGs. In particular, we develop methodology to read off possible ancestral relationships, we introduce a graphical criterion for covariate adjustment to estimate total causal effects, and we adapt the IDA and joint-IDA frameworks to estimate multi-sets of possible causal effects. We also present a simulation study that illustrates the gain in identifiability of total causal effects as the background knowledge increases. All methods are implemented in the R package pcalg.Comment: 17 pages, 6 figures, UAI 201

Cut Tree Construction from Massive Graphs

The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining, as they support various procedures related to the minimum cut, maximum flow, and connectivity. However, the crucial drawback with cut trees is the computational cost of their construction. In theory, a cut tree is built by applying a maximum flow algorithm for $n$ times, where $n$ is the number of vertices. Therefore, naive implementations of this approach result in cubic time complexity, which is obviously too slow for today's large-scale graphs. To address this issue, in the present study, we propose a new cut-tree construction algorithm tailored to real-world networks. Using a series of experiments, we demonstrate that the proposed algorithm is several orders of magnitude faster than previous algorithms and it can construct cut trees for billion-scale graphs.Comment: Short version will appear at ICDM'1

Forbidden Directed Minors and Kelly-width

Partial 1-trees are undirected graphs of treewidth at most one. Similarly, partial 1-DAGs are directed graphs of KellyWidth at most two. It is well-known that an undirected graph is a partial 1-tree if and only if it has no K_3 minor. In this paper, we generalize this characterization to partial 1-DAGs. We show that partial 1-DAGs are characterized by three forbidden directed minors, K_3, N_4 and M_5

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The demands of improving energy efficiency for high performance scientific applications arise crucially nowadays. Software-controlled hardware solutions directed by Dynamic Voltage and Frequency Scaling (DVFS) have shown their effectiveness extensively. Although DVFS is beneficial to green computing, introducing DVFS itself can incur non-negligible overhead, if there exist a large number of frequency switches issued by DVFS. In this paper, we propose a strategy to achieve the optimal energy savings for distributed matrix multiplication via algorithmically trading more computation and communication at a time adaptively with user-specified memory costs for less DVFS switches, which saves 7.5% more energy on average than a classic strategy. Moreover, we leverage a high performance communication scheme for fully exploiting network bandwidth via pipeline broadcast. Overall, the integrated approach achieves substantial energy savings (up to 51.4%) and performance gain (28.6% on average) compared to ScaLAPACK pdgemm() on a cluster with an Ethernet switch, and outperforms ScaLAPACK and DPLASMA pdgemm() respectively by 33.3% and 32.7% on average on a cluster with an Infiniband switch

The Synchronized Filtering Dataflow

In the past decade, the world has seen the rise of big data, which calls for a paradigm shift in data processing. Streaming processing, where data are processed in their spatial or temporal order, is increasingly common. Meanwhile, parallel computing has become a household term in the computing world. The combination of streaming processing and parallel computing, streaming computing, has been playing an important role in data processing. A streaming computing system is a network of nodes connected by unidirectional first-in first-out (FIFO) data channels. When a node has multiple input channels, to ensure the deterministic behavior of the whole system, synchronization is required on those channels when the node consumes data. After a streaming computing node finishes a computation, it may choose not to produce output on some of its output channels. This behavior, known as filtering, is data-dependent and unpredictable. When filtered data streams are synchronized, applications can deadlock due to empty and full channel buffers. To avoid deadlocks and ensure bounded-memory execution, we turn to model-based approaches. In this dissertation, we propose the synchronized filtering dataflow (SFDF) to model synchronization and filtering behaviors. We avoid deadlocks in SFDF applications by augmenting data streams with dummy messages. We design decentralized algorithms that compute a dummy interval for each channel during compilation time and schedule dummy messages according to the dummy intervals during runtime. The runtime parts of our algorithms are very efficient, adding little overhead to computing nodes, but computing dummy intervals could be very time-consuming on general dataflow graphs. We design efficient algorithms to compute dummy intervals for streaming applications with special topologies. In particular, we focus on series-parallel directed acyclic graphs (SP-DAGs) and CS4 DAGs, where each undirected cycle is single-source and single-sink. We further extend our work to describe a set of polyhedral constraints that define all sets of safe dummy intervals for any dataflow graphs, which gives us more flexibility to choose dummy intervals. We also provide a polynomial-time algorithm to verify the safety of given dummy intervals for SP-DAGs. Dummy messages are only one type of control message used by streaming applications. We extend our SFDF model to support more types of control message, which are precisely synchronized with data streams. We use two types of control messages, dummy message and credit message, to guarantee bounded-memory execution. We demonstrate that the extended model can help improve performance of some applications by adding filtering behavior to non-filtering applications