SUBOPTIMAL-OPTIMAL ROUTING FOR LAN INTERNETWORKING USING TRANSPARENT BRIDGES

1998 ◽  
Vol 09 (02) ◽  
pp. 139-156 ◽  
Author(s):  
ROMAN GARCIA ◽  
JOSE DUATO
Keyword(s):  
Spanning Tree ◽  
Optimal Routing ◽  
Current Standard ◽  
Worst Case ◽  
Network Bandwidth ◽  
Strongly Connected ◽  
Transparent Bridge

The current standard transparent bridge protocol IEEE-802.1D is based on the Spanning Tree (ST) algorithm. It has a very important restriction: it cannot work when the topology has active loops. Therefore, a tree is the only possible interconnection topology that can be used. The ST algorithm guarantees that the active topology is a tree discarding lines that form loops. However, because of this, network bandwidth cannot be fully utilized. Moreover, trees have a very serious bottleneck near the root. This paper proposes a new transparent bridge protocol for LAN interconnection that allows active loops. Therefore, strongly connected regular topologies like tori, hypercubes, meshes, etc., as well as irregular topologies can be used without wasting bandwidth. As loops provide alternative paths, the new protocol (named OSR for Optimal-Suboptimal Routing) uses optimal routing or, in the worst case, suboptimal routing.

scholarly journals A Combinatorial Proof of a Formula of Biane and Chapuy

10.37236/7061 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Sinho Chewi ◽  
Venkat Anantharam
Keyword(s):  
Directed Graph ◽  
Spanning Tree ◽  
Spanning Trees ◽  
Outgoing Edge ◽  
Alternative Proof ◽  
Combinatorial Proof ◽  
Tree Graph ◽  
Weighted Directed Graph ◽  
Strongly Connected

Let $G$ be a simple strongly connected weighted directed graph. Let $\mathcal{G}$ denote the spanning tree graph of $G$. That is, the vertices of $\mathcal{G}$ consist of the directed rooted spanning trees on $G$, and the edges of $\mathcal{G}$ consist of pairs of trees $(t_i, t_j)$ such that $t_j$ can be obtained from $t_i$ by adding the edge from the root of $t_i$ to the root of $t_j$ and deleting the outgoing edge from $t_j$. A formula for the ratio of the sum of the weights of the directed rooted spanning trees on $\mathcal{G}$ to the sum of the weights of the directed rooted spanning trees on $G$ was recently given by Biane and Chapuy. Our main contribution is an alternative proof of this formula, which is both simple and combinatorial.

Synchronizing Almost-Group Automata

2020 ◽  
pp. 1-22
Author(s):  
Mikhail V. Berlinkov ◽  
Cyril Nicaud
Keyword(s):  
Lower Bound ◽  
Efficient Algorithm ◽  
High Probability ◽  
Worst Case ◽  
Average Case ◽  
Model Of Computation ◽  
Letter Alphabet ◽  
Strongly Connected ◽  
Small Change ◽  
Random Automata

In this paper we address the question of synchronizing random automata in the critical settings of almost-group automata. Group automata are automata where all letters act as permutations on the set of states, and they are not synchronizing (unless they have one state). In almost-group automata, one of the letters acts as a permutation on [Formula: see text] states, and the others as permutations. We prove that this small change is enough for automata to become synchronizing with high probability. More precisely, we establish that the probability that a strongly-connected almost-group automaton is not synchronizing is [Formula: see text], for a [Formula: see text]-letter alphabet. We also present an efficient algorithm that decides whether a strongly-connected almost-group automaton is synchronizing. For a natural model of computation, we establish a [Formula: see text] worst-case lower bound for this problem ([Formula: see text] for the average case), which is almost matched by our algorithm.

PARALLEL REAL-TIME OPTIMIZATION: BEYOND SPEEDUP

1999 ◽  
Vol 09 (04) ◽  
pp. 499-509 ◽  
Author(s):  
SELIM G. AKL ◽  
Stefan D. Bruda
Keyword(s):  
Parallel Algorithm ◽  
Real Time ◽  
Spanning Tree ◽  
Optimization Problems ◽  
Minimum Weight ◽  
Parallel Computer ◽  
Worst Case ◽  
Time Optimization ◽  
Minimum Weight Spanning Tree ◽  
Real Time Optimization

Traditionally, interest in parallel computation centered around the speedup provided by parallel algorithms over their sequential counterparts. In this paper, we ask a different type of question: Can parallel computers, due to their speed, do more than simply speed up the solution to a problem? We show that for real-time optimization problems, a parallel computer can obtain a solution that is better than that obtained by a sequential one. Specifically, a sequential and a parallel algorithm are exhibited for the problem of computing the best-possible approximation to the minimum-weight spanning tree of a connected, undirected and weighted graph whose vertices and edges are not all available at the outset, but instead arrive in real time. While the parallel algorithm succeeds in computing the exact minimum-weight spanning tree, the sequential algorithm can only manage to obtain an approximate solution. In the worst case, the ratio of the weight of the solution obtained sequentially to that of the solution computed in parallel can be arbitrarily large.

scholarly journals Symbolic Coloured SCC Decomposition

2021 ◽  
pp. 64-83
Author(s):  
Nikola Beneš ◽  
Luboš Brim ◽  
Samuel Pastva ◽  
David Šafránek
Keyword(s):  
Systems Biology ◽  
Directed Graphs ◽  
Connected Components ◽  
Worst Case ◽  
Strongly Connected Components ◽  
Binary Decision ◽  
Scientific Disciplines ◽  
Experimental Implementation ◽  
Strongly Connected ◽  
Symbolic Algorithm

AbstractProblems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale.We propose a new, symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs $$O(p\cdot n\cdot \log n)$$ O ( p · n · log n ) symbolic steps, where p is the number of colours and n the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to $$2^{48}$$ 2 48 ) coloured graphs produced by models appearing in systems biology.

TOPOLOGICAL PROPERTIES OF BANK NETWORKS: THE CASE OF BRAZIL

2009 ◽  
Vol 20 (08) ◽  
pp. 1121-1143 ◽  
Author(s):  
BENJAMIN M. TABAK ◽  
DANIEL O. CAJUEIRO ◽  
THIAGO R. SERRA
Keyword(s):  
Correlation Matrix ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Foreign Banks ◽  
Topological Properties ◽  
Bank Profitability ◽  
Empirical Results ◽  
Strongly Connected

This paper investigates the topological properties of bank networks. We build the minimum spanning tree, which is based on the concept of ultrametricity, using the correlation matrix for a variety of banking variables. Empirical results suggest that the private and foreign banks tend to form clusters within the network. Furthermore, banks with different sizes are also strongly connected and tend to form clusters. These results are robust to the use of different variables to build the network, such as bank profitability, assets, equity, revenue and loans.

ON THE COMPLEXITY OF SOME ADAPTIVE POLLING ALGORITHMS IN GENERAL NETWORKS

1999 ◽  
Vol 10 (02) ◽  
pp. 211-223 ◽  
Author(s):  
SAVIO S. H. TSE ◽  
FRANCIS C. M. LAU
Keyword(s):  
Lower Bound ◽  
Spanning Tree ◽  
Worst Case ◽  
Bit Complexity ◽  
Adaptive Polling ◽  
The Cost ◽  
General Networks

We study the problem of adaptive polling in undirected general networks. Polling, also known as broadcast-confirm, consists a propagation round and a feedback round. In adaptive polling, a spanning tree of unknown topology is built dynamically during the propagation round, and feedback messages are free to choose their paths in order to adapt to traffic and fault situations. We study three adaptive polling algorithms and analyze their worst-case communication bit complexities in the propagation round. Then, we prove a lower bound on the worst-case communication bit complexity of Ω(e+n log n) in the propagation round for all algorithms of the same kind as the three algorithms we study, where n is the number of nodes, and e the number of edges. We conclude that the cost introduced into the network due to the running of an adaptive polling algorithm is mild.

STRONGER QUICKHEAPS

2011 ◽  
Vol 22 (04) ◽  
pp. 945-969
Author(s):  
GONZALO NAVARRO ◽  
RODRIGO PAREDES ◽  
PATRICIO V. POBLETE ◽  
PETER SANDERS
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Binary Search ◽  
Priority Queues ◽  
Binary Search Trees ◽  
Search Trees ◽  
Worst Case ◽  
Tree Algorithms ◽  
Amortized Complexity ◽  
Time Bounds

The Quickheap (QH) is a recent data structure for implementing priority queues which has proved to be simple and efficient in practice. It has also been shown to offer logarithmic expected amortized complexity for all of its operations. Yet, this complexity holds only when keys inserted and deleted are uniformly distributed over the current set of keys. This assumption is in many cases difficult to verify, and does not hold in some important applications such as implementing some minimum spanning tree algorithms using priority queues. In this paper we introduce an elegant model called a Leftmost Skeleton Tree (LST) that reveals the connection between QHs and randomized binary search trees, and allows us to define Randomized QHs. We prove that these offer logarithmic expected amortized complexity for all operations regardless of the input distribution. We also use LSTs in connection to α-balanced trees to achieve a practical α-Balanced QH that offers worst-case amortized logarithmic time bounds for all the operations. Both variants are much more robust than the original QHs. We show experimentally that randomized QHs behave almost as efficiently as QHs on random inputs, and that they retain their good performance on inputs where that of QHs degrades.

Belated Analyses of Three Credit-Based Adaptive Polling Algorithms

2016 ◽  
Vol 27 (05) ◽  
pp. 579-594
Author(s):  
Savio S. H. Tse
Keyword(s):  
Lower Bound ◽  
Spanning Tree ◽  
Arbitrary Point ◽  
Message Complexity ◽  
Worst Case ◽  
Average Case ◽  
Asynchronous Networks ◽  
Adaptive Polling ◽  
Point To Point ◽  
Optimal Lower Bound

We study the problem of credit-based adaptive polling in undirected arbitrary point-to-point asynchronous networks. Polling consists of two rounds, namely propagation (broadcast) and feedback (confirmation, response) rounds. By adaptive polling, a spanning tree of unknown topology is built dynamically during the propagation round, and feedback messages are free to choose their paths back to the initiator — a specific node who initiates the polling algorithm. The freedom in the feedback round relies on the use of credits in the propagation round. We re-visit three existing algorithms and analyse their average case communication bit complexities incurred by the credits in the propagation round, and these analyses match with the numerical results. We also give an optimal lower bound on the worst case bit message complexity for the case when the number of nodes in the network is unknown.

Sign in / Sign up

Export Citation Format

Share Document