K-way Balanced Graph Partitioning for Parallel Computing

In modern computing, high-performance computing (HPC) and parallel computing require most of the decision-making in terms of distributing the payloads (input) uniformly across the available set of resources, majorly processors; the former deals with the hardware and its better utilization. In parallel computing, a larger, complex problem is broken down into multiple smaller calculations and executed simultaneously on several processors. The efficient use of resources (processors) plays a vital role in achieving the maximum throughput which necessitates uniform load distribution across available processors, i.e. load balancing. The load balancing in parallel computing is modeled as a graph partitioning problem. In the graph partitioning problem, the weighted nodes represent the computing cost at each node, and the weighted edges represent the communication cost between the connected nodes. The goal is to partition the graph G into k partitions such that: I) the sum of weights on the nodes is approximately equal for each partition, and, II) the sum of weights on the edges across different partitions is minimum. In this paper, a novel node-weighted and edge-weighted k-way balanced graph partitioning (NWEWBGP) algorithm of O(n x n) is proposed. The algorithm works for all relevant values of k, meets or improves on earlier algorithms in terms of balanced partitioning and lowest edge-cut. For evaluation and validation, the outcome is compared with the ground truth benchmarks.

On the Packing Partitioning Problem on Directed Graphs

This work is aimed to continue studying the packing sets of digraphs via the perspective of partitioning the vertex set of a digraph into packing sets (which can be interpreted as a type of vertex coloring of digraphs) and focused on finding the minimum cardinality among all packing partitions for a given digraph D, called the packing partition number of D. Some lower and upper bounds on this parameter are proven, and their exact values for directed trees are given in this paper. In the case of directed trees, the proof results in a polynomial-time algorithm for finding a packing partition of minimum cardinality. We also consider this parameter in digraph products. In particular, a complete solution to this case is presented when dealing with the rooted products.

Antiferromagnetic spatial photonic Ising machine through optoelectronic correlation computing

Recently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing with SPIM. Also we exploit the gauge transformation which enables encoding the spins and the interaction strengths in a single phase-only spatial light modulator. With a simple setup, we experimentally show the ground-state-search acceleration of an antiferromagnetic model with 40000 spins in number-partitioning problem. Thus such an optoelectronic computing exhibits great programmability and scalability for the practical applications of studying statistical systems and combinatorial optimization problems.

Multi-series Time-aware Sequence Partitioning for Disease Progression Modeling

Electronic healthcare records (EHRs) are comprehensive longitudinal collections of patient data that play a critical role in modeling the disease progression to facilitate clinical decision-making. Based on EHRs, in this work, we focus on sepsis -- a broad syndrome that can develop from nearly all types of infections (e.g., influenza, pneumonia). The symptoms of sepsis, such as elevated heart rate, fever, and shortness of breath, are vague and common to other illnesses, making the modeling of its progression extremely challenging. Motivated by the recent success of a novel subsequence clustering approach: Toeplitz Inverse Covariance-based Clustering (TICC), we model the sepsis progression as a subsequence partitioning problem and propose a Multi-series Time-aware TICC (MT-TICC), which incorporates multi-series nature and irregular time intervals of EHRs. The effectiveness of MT-TICC is first validated via a case study using a real-world hand gesture dataset with ground-truth labels. Then we further apply it for sepsis progression modeling using EHRs. The results suggest that MT-TICC can significantly outperform competitive baseline models, including the TICC. More importantly, it unveils interpretable patterns, which sheds some light on better understanding the sepsis progression.

Antiferromagnetic spatial photonic Ising machine through optoelectronic correlation computing

Recently, spatial photonic Ising machines (SPIM) have been demonstrated to compute the minima of Hamiltonians for large-scale spin systems. Here we propose to implement an antiferromagnetic model through optoelectronic correlation computing with SPIM. Also we exploit the gauge transformation which enables encoding the spins and the interaction strengths in a single phase-only spatial light modulator. With a simple setup, we experimentally show the ground state search of an antiferromagnetic model with $40000$ spins in number-partitioning problem. Thus such an optoelectronic computing exhibits great programmability and scalability for the practical applications of studying statistical systems and combinatorial optimization problems.

Group Target Tracking Based on MS-MeMBer Filters

This paper presents a new group target tracking method based on the standard multi-sensor multi-target multi-Bernoulli (MS-MeMBer) filter. In the prediction step, the group structure is used to constrain the movement of the constituent members within the respective groups. Specifically, the group of members is considered as an undirected random graph. Combined with the virtual leader-follower model, the motion equation of the members within groups is formulated. In the update step, the partitioning problem of multiple sensors is transformed into a multi-dimensional assignment (MDA) problem. Compared with the original two-step greedy partitioning mechanism, the MDA algorithm achieves better measurement partitions in group target tracking scenarios. To evaluate the performance of the proposed method, a simulation scenario including group splitting and merging is established. Results show that, compared with the standard MS-MeMBer filter, our method can effectively estimate the cardinality of members and groups at the cost of increasing computational load. The filtering accuracy of the proposed method outperforms that of the MS-MeMBer filter.