scholarly journals Resilient Capacity-Aware Routing

2021 ◽  
pp. 411-429
Author(s):  
Stefan Schmid ◽  
Nicolas Schnepf ◽  
Jiří Srba
Keyword(s):  
Communication Networks ◽  
Search Algorithm ◽  
Shortest Paths ◽  
Capacity Constraints ◽  
High Availability ◽  
Worst Case ◽  
Shortest Path Routing ◽  
Link Failures ◽  
Algorithmic Question ◽  
Improved Performance

AbstractTo ensure a high availability, communication networks provide resilient routing mechanisms that quickly change routes upon failures. However, a fundamental algorithmic question underlying such mechanisms is hardly understood: how to verify whether a given network reroutes flows along feasible paths, without violating capacity constraints, for up to k link failures? We chart the algorithmic complexity landscape of resilient routing under link failures, considering shortest path routing based on link weights as e.g. deployed in the ECMP protocol. We study two models: a pessimistic model where flows interfere in a worst-case manner along equal-cost shortest paths, and an optimistic model where flows are routed in a best-case manner, and we present a complete picture of the algorithmic complexities. We further propose a strategic search algorithm that checks only the critical failure scenarios while still providing correctness guarantees. Our experimental evaluation on a benchmark of Internet and datacenter topologies confirms an improved performance of our strategic search by several orders of magnitude.

scholarly journals Betweenness centrality profiles in trees

2017 ◽  
Vol 5 (5) ◽  
pp. 776-794
Author(s):  
Benjamin Fish ◽  
Rahul Kushwaha ◽  
György Turán
Keyword(s):  
Betweenness Centrality ◽  
Shortest Paths ◽  
Random Trees ◽  
Experimental Results ◽  
Basic Notion ◽  
Worst Case ◽  
Scale Free ◽  
Order Of Magnitude

Abstract Betweenness centrality of a vertex in a graph measures the fraction of shortest paths going through the vertex. This is a basic notion for determining the importance of a vertex in a network. The $k$-betweenness centrality of a vertex is defined similarly, but only considers shortest paths of length at most $k$. The sequence of $k$-betweenness centralities for all possible values of $k$ forms the betweenness centrality profile of a vertex. We study properties of betweenness centrality profiles in trees. We show that for scale-free random trees, for fixed $k$, the expectation of $k$-betweenness centrality strictly decreases as the index of the vertex increases. We also analyse worst-case properties of profiles in terms of the distance of profiles from being monotone, and the number of times pairs of profiles can cross. This is related to whether $k$-betweenness centrality, for small values of $k$, may be used instead of having to consider all shortest paths. Bounds are given that are optimal in order of magnitude. We also present some experimental results for scale-free random trees.

scholarly journals Motion Estimation Architecture Using Efficient Adder-Compressors for HDTV Video Coding

2010 ◽  
Vol 5 (1) ◽  
pp. 78-88 ◽  
Author(s):  
Marcelo Porto ◽  
André Silva ◽  
Sergo Almeida ◽  
Eduardo Da Costa ◽  
Sergio Bampi
Keyword(s):  
Motion Estimation ◽  
Real Time ◽  
Search Algorithm ◽  
Absolute Difference ◽  
High Definition ◽  
Case Processing ◽  
Worst Case ◽  
Average Case ◽  
High Definition Television ◽  
Internal Structures

This paper presents real time HDTV (High Definition Television) architecture for Motion Estimation (ME) using efficient adder compressors. The architecture is based on the Quarter Sub-sampled Diamond Search algorithm (QSDS) with Dynamic Iteration Control (DIC) algorithm. The main characteristic of the proposed architecture is the large amount of Processing Units (PUs) that are used to calculate the SAD (Sum of Absolute Difference) metric. The internal structures of the PUs are composed by a large number of addition operations to calculate the SADs. In this paper, efficient 4-2 and 8-2 adder compressors are used in the PUs architecture to achieve the performance to work with HDTV (High Definition Television) videos in real time at 30 frames per second. These adder compressors enable the simultaneous addition of 4 and 8 operands respectively. The PUs, using adder compressors, were applied to the ME architecture. The implemented architecture was described in VHDL and synthesized to FPGA and, with Leonardo Spectrum tool, to the TSMC 0.18μm CMOS standard cell technology. Synthesis results indicate that the new QSDS-DIC architecture reach the best performance result and enable gains of 12% in terms of processing rate. The architecture can reach real time for full HDTV (1920x1080 pixels) in the worst case processing 65 frames per second, and it can process 269 HDTV frames per second in the average case.

scholarly journals A new algorithm for fixed point quantum search

2006 ◽  
Vol 6 (6) ◽  
pp. 483-494
Author(s):  
T. Tulsi ◽  
L.K. Grover ◽  
A. Patel
Keyword(s):  
Fixed Point ◽  
Error Probability ◽  
Search Algorithm ◽  
Quantum Search ◽  
Worst Case ◽  
Average Case ◽  
Standard Quantum ◽  
Quantum Search Algorithm ◽  
Monotonic Convergence ◽  
Worst Case Behavior

The standard quantum search lacks a feature, enjoyed by many classical algorithms, of having a fixed point, i.e. monotonic convergence towards the solution. Recently a fixed point quantum search algorithm has been discovered, referred to as the Phase-\pi/3 search algorithm, which gets around this limitation. While searching a database for a target state, this algorithm reduces the error probability from \epsilon to \epsilon^{2q+1} using q oracle queries, which has since been proved to be asymptotically optimal. A different algorithm is presented here, which has the same worst-case behavior as the Phase-\pi/3 search algorithm but much better average-case behavior. Furthermore the new algorithm gives \epsilon^{2q+1} convergence for all integral q, whereas the Phase-\pi/3 search algorithm requires q to be (3^{n}-1)/2 with n a positive integer. In the new algorithm, the operations are controlled by two ancilla qubits, and fixed point behavior is achieved by irreversible measurement operations applied to these ancillas. It is an example of how measurement can allow us to bypass some restrictions imposed by unitarity on quantum computing.

RANDOMIZED MOBILE AGENT BASED ROUTING IN WIRELESS NETWORKS

2001 ◽  
Vol 12 (03) ◽  
pp. 365-384 ◽  
Author(s):  
MARC BUI ◽  
SAJAL K. DAS ◽  
AJOY K. DATTA ◽  
DAI THO NGUYEN
Keyword(s):  
Mobile Agent ◽  
Mobile Networks ◽  
Mobile Agents ◽  
Shortest Paths ◽  
Mobile Nodes ◽  
Shortest Path Routing ◽  
Link State ◽  
Novel Approach ◽  
Link Cost ◽  
Routing Tables

We propose a novel approach for shortest path routing in wireless mobile networks. The approach makes use of n mobile agents initially launched from n mobile nodes forming the network. The agents move randomly from node to node and update routing information as they go. The approach is presented in this paper with two protocols. Both of them exhibit good performance in terms of the network and computing resource consumptions. The first protocol relies on independent mobile agents and imposes a minimum bandwidth requirement on individual mobile agents. Each agent carries the link state of its creator and this information remains unchanged except when the mobile agent returns to the home node. The second protocol is a refinement of the first protocol, with some form of interaction between the mobile agents. Each agent maintains the routing table of its creator instead of link state. The randomly walking agents spread the update information and compute the shortest paths via exchanging network state information between the routing tables they carry and the routing tables at the nodes they traverse. The correctness of the protocols is proven. Our analysis shows that the agent cooperation improves the system performance when dealing with topology and link cost changes.

(ℓ, k)-ROUTING ON PLANE GRIDS

2009 ◽  
Vol 10 (01n02) ◽  
pp. 27-57
Author(s):  
FLORIAN HUC ◽  
IGNASI SAU ◽  
JANEZ ŽEROVNIK
Keyword(s):  
Communication Networks ◽  
Routing Algorithms ◽  
Full Duplex ◽  
Packet Routing ◽  
Routing Problem ◽  
Shortest Path Routing ◽  
Running Time ◽  
Half Duplex ◽  
Hexagonal Grids ◽  
Permutation Routing

The packet routing problem plays an essential role in communication networks. It involves how to transfer data from some origins to some destinations within a reasonable amount of time. In the (ℓ, k)-routing problem, each node can send at most ℓ packets and receive at most k packets. Permutation routing is the particular case ℓ = k = 1. In the r-central routing problem, all nodes at distance at most r from a fixed node v want to send a packet to v. In this article we study the permutation routing, the r-central routing and the general (ℓ, k)-routing problems on plane grids, that is square grids, triangular grids and hexagonal grids. We use the store-and-forward Δ-port model, and we consider both full and half-duplex networks. We first survey the existing results in the literature about packet routing, with special emphasis on (ℓ, k)-routing on plane grids. Our main contributions are the following: 1. Tight permutation routing algorithms on full-duplex hexagonal grids, and half duplex triangular and hexagonal grids. 2. Tight r-central routing algorithms on triangular and hexagonal grids. 3. Tight (k, k)-routing algorithms on square, triangular and hexagonal grids. 4. Good approximation algorithms (in terms of running time) for (ℓ, k)-routing on square, triangular and hexagonal grids, together with new lower bounds on the running time of any algorithm using shortest path routing. These algorithms are all completely distributed, i.e., can be implemented independently at each node. Finally, we also formulate the (ℓ, k)-routing problem as a WEIGHTED EDGE COLORING problem on bipartite graphs.

scholarly journals Local Search with Dynamic-Threshold Configuration Checking and Incremental Neighborhood Updating for Maximum k-plex Problem

2020 ◽  
Vol 34 (03) ◽  
pp. 2343-2350 ◽  
Author(s):  
Peilin Chen ◽  
Hai Wan ◽  
Shaowei Cai ◽  
Jia Li ◽  
Haicheng Chen
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Promising Result ◽  
Dynamic Threshold ◽  
Local Search Algorithm ◽  
Local Search Algorithms ◽  
Worst Case ◽  
Massive Graphs ◽  
Configuration Checking ◽  
Novel Strategy

The Maximum k-plex Problem is an important combinatorial optimization problem with increasingly wide applications. In this paper, we propose a novel strategy, named Dynamic-threshold Configuration Checking (DCC), to reduce the cycling problem of local search. Due to the complicated neighborhood relations, all the previous local search algorithms for this problem spend a large amount of time in identifying feasible neighbors in each step. To further improve the performance on dense and challenging instances, we propose Double-attributes Incremental Neighborhood Updating (DINU) scheme which reduces the worst-case time complexity per iteration from O(|V|⋅ΔG) to O(k · Δ‾G). Based on DCC strategy and DINU scheme, we develop a local search algorithm named DCCplex. According to the experiment result, DCCplex shows promising result on DIMACS and BHOSLIB benchmark as well as real-world massive graphs. Especially, DCCplex updates the lower bound of the maximum k-plex for most dense and challenging instances.

scholarly journals Algorithms for Finding Shortest Paths in Networks with Vertex Transfer Penalties

Algorithms ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 269 ◽  
Author(s):  
Rhyd Lewis
Keyword(s):  
Waiting Times ◽  
Shortest Paths ◽  
Dijkstra’S Algorithm ◽  
Weighted Graphs ◽  
Worst Case ◽  
Sparse Graphs ◽  
Graph Expansion ◽  
Advantages And Disadvantages ◽  
Dijkstra's Algorithm ◽  
Dense Graphs

In this paper we review many of the well-known algorithms for solving the shortest path problem in edge-weighted graphs. We then focus on a variant of this problem in which additional penalties are incurred at the vertices. These penalties can be used to model things like waiting times at road junctions and delays due to transfers in public transport. The usual way of handling such penalties is through graph expansion. As an alternative, we propose two variants of Dijkstra’s algorithm that operate on the original, unexpanded graph. Analyses are then presented to gauge the relative advantages and disadvantages of these methods. Asymptotically, compared to using Dijkstra’s algorithm on expanded graphs, our first variant is faster for very sparse graphs but slower with dense graphs. In contrast, the second variant features identical worst-case run times.

Design of High Speed Reconfigurable Distributed Life Time Efficient Routing Algorithm in Wireless Sensor Network

2020 ◽  
Vol 17 (9) ◽  
pp. 3860-3866
Author(s):  
M. L. Umashankar ◽  
S. Mallikarjunaswamy ◽  
M. V. Ramakrishna
Keyword(s):  
Shortest Path ◽  
High Speed ◽  
Routing Algorithm ◽  
Shortest Paths ◽  
Life Time ◽  
Wireless Sensor ◽  
Signal Interference ◽  
Energy Efficient Routing ◽  
Shortest Path Routing ◽  
Routing Techniques

Designing an energy-efficient routing makes the Wireless Sensor Networks (WSN) more effective and attractive for different applications. The WSN communication system power consumption mainly depends on three aspects such as routing cost computation, signal interference, and routing distance. All three factors are equally important in order to improve the network performance. The system reliability and deployment cost depends on the energy efficiency of the WSN. The energy related cost assignment and shortest paths identification are used in existing routing techniques. In the existing routing techniques maximum achievable lifetime and optimal link cost are low. Hence greatest possible performance can be achieved in distributed routing algorithm by finding shortest path. Maximum lifetime and best cost link can be generally obtained using distributed shortest path routing algorithm. In this paper high speed reconfigurable distributed Lifetime-Efficient Routing algorithm is designed to provide route selection outline with low complexity and obtain better performance compared to existing routing algorithm.

scholarly journals AND/OR Multi-Valued Decision Diagrams (AOMDDs) for Graphical Models

2008 ◽  
Vol 33 ◽  
pp. 465-519 ◽  
Author(s):  
R. Mateescu ◽  
R. Dechter ◽  
R. Marinescu
Keyword(s):  
Graphical Models ◽  
Probabilistic Models ◽  
Graphical Model ◽  
Search Algorithm ◽  
Decision Diagrams ◽  
Worst Case ◽  
Ordered Binary Decision Diagrams ◽  
Search Spaces ◽  
Function Decomposition ◽  
Decomposition Structure

Inspired by the recently introduced framework of AND/OR search spaces for graphical models, we propose to augment Multi-Valued Decision Diagrams (MDD) with AND nodes, in order to capture function decomposition structure and to extend these compiled data structures to general weighted graphical models (e.g., probabilistic models). We present the AND/OR Multi-Valued Decision Diagram (AOMDD) which compiles a graphical model into a canonical form that supports polynomial (e.g., solution counting, belief updating) or constant time (e.g. equivalence of graphical models) queries. We provide two algorithms for compiling the AOMDD of a graphical model. The first is search-based, and works by applying reduction rules to the trace of the memory intensive AND/OR search algorithm. The second is inference-based and uses a Bucket Elimination schedule to combine the AOMDDs of the input functions via the the APPLY operator. For both algorithms, the compilation time and the size of the AOMDD are, in the worst case, exponential in the treewidth of the graphical model, rather than pathwidth as is known for ordered binary decision diagrams (OBDDs). We introduce the concept of semantic treewidth, which helps explain why the size of a decision diagram is often much smaller than the worst case bound. We provide an experimental evaluation that demonstrates the potential of AOMDDs.

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