Search

With the huge demand for graph analytics in many real-world applications, massive iterative graph processing jobs are concurrently performed on the same graphs and suffer from significant high data access cost. To lower the data access cost toward high performance, several out-of-core concurrent graph processing solutions are recently designed to handle concurrent jobs by enabling these jobs to share the accesses of the same graph data. However, the set of active vertices in each partition are usually different for various concurrent jobs and also evolve with time, where some high-degree ones (or called hub-vertices) of these active vertices require more iterations to converge due to the power-law property of real-world graphs. In consequence, existing solutions still suffer from much unnecessary I/O traffic, because they have to entirely load each partition into the memory for concurrent jobs even if most vertices in this partition are inactive and may be shared by a few jobs. In this paper, we propose an efficient structure-aware storage system, called GraphSO, for higher throughput of the execution of concurrent graph processing jobs. It can be integrated into existing out-of-core graph processing systems to promote the execution efficiency of concurrent jobs with lower I/O overhead. The key design of GraphSO is a fine-grained storage management scheme. Specifically, it logically divides the partitions of existing graph processing systems into a series of small same-sized chunks. At runtime, these small chunks with active vertices are judiciously loaded by GraphSO to construct new logical partitions (i.e., each logical partition is a subset of active chunks) for existing graph processing systems to handle, where the most-frequently-used chunks are preferentially loaded to construct the logical partitions and the other ones are delayed to wait to be required by more jobs. In this way, it can effectively spare the cost of loading the graph data associated with the inactive vertices with low repartitioning overhead and can also enable the loaded graph data to be fully shared by concurrent jobs. Moreover, GraphSO also designs a buffering strategy to efficiently cache the most-frequently-used chunks in the main memory to further minimize the I/O traffic by avoiding repeated load of them. Experimental results show that GraphSO improves the throughput of GridGraph, GraphChi, X-Stream, DynamicShards, LUMOS, Graphene, and Wonderland by 1.4-3.5 times, 2.1-4.3 times, 1.9-4.1 times, 1.9-2.9 times, 1.5-3.1 times, 1.3-1.5 times, and 1.3-2.7 times after integrating with them, respectively. [ABSTRACT FROM AUTHOR]

The past decade has seen growing importance being attached to the Completely Independent Spanning Trees (CISTs). The CISTs can facilitate many network functionalities, and the existence and construction schemes of CISTs in various networks can be an indicator of the network's robustness. In this paper, we establish the number of CISTs that can be constructed in the line graph of the complete graph $K_n$ K n (denoted $L(K_n)$ L (K n) , for $n\geq 4$ n ≥ 4 ), and present an algorithm to construct the optimal (i.e., maximal) number of CISTs in $L(K_n)$ L (K n) . The $L(K_n)$ L (K n) is a special class of SWCube [13], an architectural model proposed for data center networks. Our construction algorithm is also implemented to verify its validity. [ABSTRACT FROM AUTHOR]

The Hidden Weighted Bit function plays an important role in the study of classical models of computation. A common belief is that this function is exponentially hard to implement using reversible ancilla-free circuits, even though introducing a small number of ancillae allows a very efficient implementation. In this paper, we refute the exponential hardness conjecture by developing a polynomial-size reversible ancilla-free circuit computing the Hidden Weighted Bit function. Our circuit has size $O(n^{6.42})$ O (n 6. 42) , where $n$ n is the number of input bits. We also show that the Hidden Weighted Bit function can be computed by a quantum ancilla-free circuit of size $O(n^2)$ O (n 2) . The technical tools employed come from a combination of Theoretical Computer Science (Barrington's theorem) and Physics (simulation of fermionic Hamiltonians) techniques. [ABSTRACT FROM AUTHOR]