A Path-Counter Method for Fault-Tolerant Minimal Routing Algorithms in 2D Mesh

2017 ◽  
Vol 27 (04) ◽  
pp. 1850054 ◽  
Author(s):  
Hongzhi Zhao ◽  
Qiang Wang ◽  
Ke Xiong ◽  
Songwen Pei
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Fault Tolerant ◽  
Routing Algorithms ◽  
Destination Node ◽  
Counter Method ◽  
Counting Procedure ◽  
Fault Block ◽  
Path Counting ◽  
Fault Distribution

Fault-tolerant Manhattan routing algorithms aim at finding a Manhattan path between the source and destination nodes and route around all faulty nodes. However, besides faulty nodes, some nonfaulty nodes that are helpless to make up a fault-tolerant Manhattan path should also be routed around. How to label such nonfaulty nodes efficiently is a major challenge. We propose a path-counter method. It can label such nodes with low time-complexity by counting every node’s fault-tolerant Manhattan paths to the source or destination node. During the path-counting procedure, no available nodes will be sacrificed under arbitrary fault distribution. Compared with fault-block model based work, our proposed method is independent of fault distribution, so its computational complexity is very low.

ON THE COMPUTATIONAL COMPLEXITY OF ROUTING IN FAULTY K-ARY N-CUBES AND HYPERCUBES

2012 ◽  
Vol 22 (01) ◽  
pp. 1250003
Author(s):  
IAIN A. STEWART
Keyword(s):  
Computational Complexity ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Routing Algorithms ◽  
Source Node ◽  
Destination Node ◽  
Underlying Graph

We equate a routing algorithm in a (faulty) interconnection network whose underlying graph is a k-ary n-cube or a hypercube, that attempts to route a packet from a fixed source node to a fixed destination node, with the sub-digraph of (healthy) links potentially usable by this routing algorithm as it attempts to route the packet. This gives rise to a naturally defined problem, parameterized by this routing algorithm, relating to whether a packet can be routed from a given source node to a given destination node in one of our interconnection networks in which there are (possibly exponentially many) faulty links. We show that there exist such problems that are PSPACE-complete (all are solvable in PSPACE) but that there are (existing and popular) routing algorithms for which the computational complexity of the corresponding problem is significantly easier (yet still computationally intractable).

Latency, Throughput and Power Aware Adaptive NoC Routing on Orthogonal Convex Faulty Region

2019 ◽  
Vol 28 (04) ◽  
pp. 1950055 ◽  
Author(s):  
Munshi Mostafijur Rahaman ◽  
Prasun Ghosal ◽  
Tuhin Subhra Das
Keyword(s):  
Performance Enhancement ◽  
Fault Tolerant ◽  
Routing Algorithms ◽  
Communication Process ◽  
Block Boundary ◽  
Fault Block ◽  
Average Latency ◽  
Virtual Boundary ◽  
And Performance ◽  
On Chip

Reliability of a Network-on-Chip (NoC) relies vastly upon the efficiency of handling faults. Faults those lead to trouble during on-chip communication process are basically of two types namely soft and hard. Here, hard faults are considered. Hard faults may be caused due to failure of links, routers, or other processing units. These are mainly dealt with fault-tolerant routing algorithms or by employing redundant hardware. Multiple faulty nodes are being avoided by acquiring region-based approaches. Most of the fault-tolerant routing techniques are designed on homogeneous faulty regions where some active nodes also act as deactivated nodes to build the region homogeneous. On the other hand, adaptive routing on nonhomogeneous faulty regions increases load on its boundary and most of them does not assure deadlock freeness. This paper proposes a deadlock-free adaptive fault-tolerant NoC routing named F-Route-NoC-Mesh (FRNM) ignoring any virtual channel on orthogonal convex faulty regions. Contributions of this work focus on balancing network traffic by assuming a virtual faulty block boundary and routing packets through this virtual boundary. Destination does not exist within that virtual faulty block regions to reduce load on the boundary of orthogonal faulty regions. Thus, this work is aimed at acquiring proper incorporation of procedures being able to reach fault-tolerant degree, routing efficiency and performance enhancement. Using the proposed algorithm (FRNM), a fault block model-based approach is developed. Significant improvements of average latency (43.37% to 60.44%), average throughput (4.18% to 90.81%) and power consumption (5.93% to 33.28%) are achieved over the state-of-the-art by using a cycle accurate simulator.

scholarly journals On Quantum Algorithm for Binary Search and Its Computational Complexity

2015 ◽  
Vol 22 (03) ◽  
pp. 1550019 ◽  
Author(s):  
S. Iriyama ◽  
M. Ohya ◽  
I.V. Volovich
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Quantum Algorithm ◽  
Binary Search ◽  
Search Problem

A new quantum algorithm for the search problem and its computational complexity are discussed. Its essential part is the use of the so-called chaos amplifier, [8, 9, 10, 13]. It is shown that for the search problem containing [Formula: see text] objects time complexity of the method is polynomial in [Formula: see text].

scholarly journals Biclique Cryptanalysis on the Full Crypton-256 and mCrypton-128

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Junghwan Song ◽  
Kwanhyung Lee ◽  
Hwanjin Lee
Keyword(s):  
Computational Complexity ◽  
Bipartite Graph ◽  
Time Complexity ◽  
Computational Time

Biclique cryptanalysis is an attack which reduces the computational complexity by finding a biclique which is a kind of bipartite graph. We show a single-key full-round attack of the Crypton-256 and mCrypton-128 by using biclique cryptanalysis. In this paper, 4-round bicliques are constructed for Crypton-256 and mCrypton-128. And these bicliques are used to recover master key for the full rounds of Crypton-256 and mCrypton-128 with the computational complexities of 2253.78and 2126.5, respectively. This is the first known single-key full-round attack on the Crypton-256. And our result on the mCrypton-128 has superiority over known result of biclique cryptanalysis on the mCrypton-128 which constructs 3-round bicliques in terms of computational time complexity.

scholarly journals NOISE-BASED LOGIC: WHY NOISE? A COMPARATIVE STUDY OF THE NECESSITY OF RANDOMNESS OUT OF ORTHOGONALITY

2012 ◽  
Vol 11 (04) ◽  
pp. 1250021 ◽  
Author(s):  
HE WEN ◽  
LASZLO B. KISH
Keyword(s):  
Computational Complexity ◽  
Comparative Study ◽  
Power Dissipation ◽  
Time Complexity ◽  
Logic Systems ◽  
Sinusoidal Signals ◽  
Better Than

Although noise-based logic shows potential advantages of reduced power dissipation and the ability of large parallel operations with low hardware and time complexity the question still persist: Is randomness really needed out of orthogonality? In this Letter, after some general thermodynamical considerations, we show relevant examples where we compare the computational complexity of logic systems based on orthogonal noise and sinusoidal signals, respectively. The conclusion is that in certain special-purpose applications noise-based logic is exponentially better than its sinusoidal version: Its computational complexity can be exponentially smaller to perform the same task.

Enhanced fault tolerant routing algorithms using a concept of “balanced ring”

2007 ◽  
Vol 53 (12) ◽  
pp. 902-912 ◽  
Author(s):  
Huaxi Gu ◽  
Jie Zhang ◽  
Kun Wang ◽  
Zengji Liu ◽  
Guochang Kang
Keyword(s):  
Fault Tolerant ◽  
Routing Algorithms
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