Enumerating Graph Partitions Without Too Small Connected Components Using Zero-suppressed Binary and Ternary Decision Diagrams

Partitioning a graph into balanced components is important for several applications. For multi-objective problems, it is useful not only to find one solution but also to enumerate all the solutions with good values of objectives. However, there are a vast number of graph partitions in a graph, and thus it is difficult to enumerate desired graph partitions efficiently. In this paper, an algorithm to enumerate all the graph partitions such that all the weights of the connected components are at least a specified value is proposed. To deal with a large search space, we use zero-suppressed binary decision diagrams (ZDDs) to represent sets of graph partitions and we design a new algorithm based on frontier-based search, which is a framework to directly construct a ZDD. Our algorithm utilizes not only ZDDs but also ternary decision diagrams (TDDs) and realizes an operation which seems difficult to be designed only by ZDDs. Experimental results show that the proposed algorithm runs up to tens of times faster than an existing state-of-the-art algorithm

Performance analysis of large-scale parallel-distributed processing with backup tasks for cloud computing

In cloud computing, a large-scale parallel-distributed processing service is provided where a huge task is split into a number of subtasks and those subtasks are processed on a cluster of machines called workers. In such a processing service, a worker which takes a long time for processing a subtask makes the response time long (the issue of stragglers). One of efficient methods to alleviate this issue is to execute the same subtask by another worker in preparation for the slow worker (backup tasks). In this paper, we consider the efficiency of backup tasks. We model the task-scheduling server as a single-server queue, in which the server consists of a number of workers. When a task enters the server, the task is split into subtasks, and each subtask is served by its own worker and an alternative distinct worker. In this processing, we explicitly derive task processing time distributions for the two cases that the subtask processing time of a worker obeys Weibull or Pareto distribution. We compare the mean response time and the total processing time under backup-task scheduling with those under normal scheduling. Numerical examples show that the efficiency of backup-task scheduling significantly depends on workers' processing time distribution

Measurement of high-energy cosmic-ray electrons with a Polar Patrol Balloon

One of the major purpose of recent cosmic-ray studies is to know the origin, acceleration mechanism and propagation properties inside the Galaxy. Along this line many efforts have been spent to observe a precise spectrum of the electron component of cosmic-rays. The main difficulty to study high-energy electrons is the detection of these electrons. The flux is much lower than the abundant proton component, and we need an observation of long duration and a detector with a high rejection power against the background protons. We propose to carry a newly developed scintillating-fiber detector on the Polar Patrol Balloon (PPB) and to expose it for 30 days. The goal of this observation is to determine a definite electron energy-spectrum ranging from 10 GeV to TeV region based on a high statistical accuracy with a long exposure by the PPB. In the result, we can expect to obtain direct evidence for the origin of high-energy electrons and a precise knowledge of their propagation in the Galaxy including solar modulation effects on the electron flux

DAO voting mechanism resistant to whale and collusion problems

With the widespread adoption of blockchain technology, a novel organizational structure known as Decentralized Autonomous Organizations (DAOs) has attracted considerable attention. DAOs facilitate decision-making through member voting, realizing the governance in a decentralized manner. However, DAOs face unique challenges compared to traditional organization. This paper focuses on two key challenges of governance within DAOs: the whale problem and collusion issue. The whale problem is characterized by the concentration of power among specific members, while for the collusion problem, voting results are distorted by fraudulent collaboration. In terms of voting, we consider Quadratic Voting, a voting system expected to deter the concentration of voting power among a subset of participants, analyzing its resistance to the collusion problem. We show with numerical examples that in comparison to Linear Voting, Quadratic Voting lacks resistance to collusion. Then, we propose a voting mechanism that integrates Quadratic Voting with the Vote escrow tokens, demonstrating the mitigation of the whale problem while acquiring resilience to collusion in the decision-making process. The numerical examples confirm the high efficacy of our proposed model