On the Competitiveness of Oblivious Routing: A Statistical View

2021 ◽  
Vol 11 (20) ◽  
pp. 9408
Author(s):  
Gábor Németh
Keyword(s):  
Performance Measures ◽  
Adaptive Algorithm ◽  
Competitive Ratio ◽  
Directed Graphs ◽  
Expected Value ◽  
Undirected Graphs ◽  
Worst Case ◽  
Oblivious Routing ◽  
Performance Penalty ◽  
Open Question

Oblivious routing is a static algorithm for routing arbitrary user demands with the property that the competitive ratio, the proportion of the maximum congestion to the best possible congestion, is minimal. Oblivious routing turned out surprisingly efficient in this worst-case sense: in undirected graphs, we pay only a logarithmic performance penalty, and this penalty is usually smaller than 2 in directed graphs as well. However, compared to an optimal adaptive algorithm, which never causes congestion when subjected to a routable demand, oblivious routing surely has congestion. The open question is of how often is the network in a congested state. In this paper, we study two performance measures naturally arising in this context: the probability of congestion and the expected value of congestion. Our main result is the finding that, in certain directed graphs on n nodes, the probability of congestion approaches 1 in some undirected graphs, despite the competitive ratio being O(1).

The Bursty Steiner Tree Problem

2017 ◽  
Vol 28 (07) ◽  
pp. 869-887
Author(s):  
Gokarna Sharma ◽  
Costas Busch
Keyword(s):  
Lower Bound ◽  
Steiner Tree ◽  
Competitive Ratio ◽  
Directed Graphs ◽  
Steiner Tree Problem ◽  
Undirected Graphs ◽  
Tight Bound ◽  
Trade Offs ◽  
Single Burst ◽  
First Results

We introduce and study a new Steiner tree problem variation called the bursty Steiner tree problem where new nodes arrive into bursts. This is an online problem which becomes the well-known online Steiner tree problem if the number of nodes in each burst is exactly one and becomes the classic Steiner tree problem if all the nodes appear in a single burst. In undirected graphs, we provide a tight bound of [Formula: see text] on the competitive ratio for this problem, where [Formula: see text] is the total number of nodes to be connected and [Formula: see text] is the total number of different bursts. In directed graphs of bounded edge asymmetry [Formula: see text], we provide a competitive ratio for this problem with a gap of [Formula: see text] factor between the lower bound and the upper bound. We also show that a tight bound of [Formula: see text] on the competitive ratio can be obtained for a bursty variation of the terminal Steiner tree problem. These are the first results that provide clear performance trade-offs for a novel Steiner tree problem variation that subsumes both of its online and classic versions.

Online peak-aware energy scheduling with untrusted advice

2021 ◽  
Vol 1 (1) ◽  
pp. 59-77
Author(s):  
Russell Lee ◽  
Jessica Maghakian ◽  
Mohammad Hajiesmaili ◽  
Jian Li ◽  
Ramesh Sitaraman ◽  
...  
Keyword(s):  
Competitive Ratio ◽  
Energy Demand ◽  
Large Scale ◽  
Performance Metrics ◽  
Randomized Algorithm ◽  
Deterministic Algorithm ◽  
Pareto Optimal ◽  
Energy Prices ◽  
Worst Case ◽  
Cost Of Energy

This paper studies the online energy scheduling problem in a hybrid model where the cost of energy is proportional to both the volume and peak usage, and where energy can be either locally generated or drawn from the grid. Inspired by recent advances in online algorithms with Machine Learned (ML) advice, we develop parameterized deterministic and randomized algorithms for this problem such that the level of reliance on the advice can be adjusted by a trust parameter. We then analyze the performance of the proposed algorithms using two performance metrics: robustness that measures the competitive ratio as a function of the trust parameter when the advice is inaccurate, and consistency for competitive ratio when the advice is accurate. Since the competitive ratio is analyzed in two different regimes, we further investigate the Pareto optimality of the proposed algorithms. Our results show that the proposed deterministic algorithm is Pareto-optimal, in the sense that no other online deterministic algorithms can dominate the robustness and consistency of our algorithm. Furthermore, we show that the proposed randomized algorithm dominates the Pareto-optimal deterministic algorithm. Our large-scale empirical evaluations using real traces of energy demand, energy prices, and renewable energy generations highlight that the proposed algorithms outperform worst-case optimized algorithms and fully data-driven algorithms.

Revised Attributes

2015 ◽  
pp. 196-214
Keyword(s):  
Performance Measures ◽  
Business Performance ◽  
Relative Advantage ◽  
Pilot Studies ◽  
Learning Capability ◽  
Financial Measures ◽  
Management Learning ◽  
Communication Capability ◽  
Business Performance Measures ◽  
Open Question

This chapter is conducted with the intention to investigate the relevancy of the attributes to the five constructs of the model. The discussion in this section is basing on the information and the key findings according to the content of these interviews six pilot studies and the open question' respondents collected from 395 questionnaires survey and other government and Industry Association documents. The revised attributes of trust is based on contractual trust, competence trust, goodwill trust and benevolence. Relationship management, learning capability, communication capability and innovation capability are selected as the main attributes of the organizational capacities in relation to inter-organizational collaboration. The five typical attributes in the DOI theory are selected for measuring e-business diffusion, which are: relative advantage, complexity, trialability and observability. Organizational effectiveness, product and service measure, financial measures, market measure and customer satisfaction measure are mainly perceived as business performance measures.

scholarly journals Robust Optimization Approach to Process Flexibility Designs with Contribution Margin Differentials

2020 ◽  
Author(s):  
Shixin Wang ◽  
Xuan Wang ◽  
Jiawei Zhang
Keyword(s):  
Robust Optimization ◽  
Performance Measures ◽  
Broad Class ◽  
Problem Definition ◽  
Partial Ordering ◽  
Group Index ◽  
Optimization Approach ◽  
Worst Case ◽  
Process Flexibility ◽  
Long Chain

Problem definition: The theoretical investigation of the effectiveness of limited flexibility has mainly focused on a performance metric that is based on the maximum sales in units. However, this could lead to substantial profit losses when the maximum sales metric is used to guide flexibility designs while the products have considerably large profit margin differences. Academic/practical relevance: We address this issue by introducing margin differentials into the analysis of process flexibility designs, and our results can provide useful guidelines for the evaluation and design of flexibility configurations when the products have heterogeneous margins. Methodology: We adopt a robust optimization framework and study process flexibility designs from the worst-case perspective by introducing the dual margin group index (DMGI). Results and managerial implications: We show that a general class of worst-case performance measures can be expressed as functions of a design’s DMGIs and the given uncertainty set. Moreover, the DMGIs lead to a partial ordering that enables us to compare the worst-case performance of different designs. Applying these results, we prove that under the so-called partwise independently symmetric uncertainty sets and a broad class of worst-case performance measures, the alternate long-chain design is optimal among all long-chain designs with equal numbers of high-profit products and low-profit products. Finally, we develop a heuristic based on the DMGIs to generate effective flexibility designs when products exhibit margin differentials.

ON THE LOWER BOUND OF THE COMPETITIVE RATIO FOR THE WEIGHTED ONLINE ROOMMATES PROBLEM

2010 ◽  
Vol 02 (02) ◽  
pp. 257-262
Author(s):  
SATYAJIT BANERJEE
Keyword(s):  
Lower Bound ◽  
Competitive Ratio ◽  
Deterministic Algorithm ◽  
Weighted Version ◽  
Worst Case ◽  
Competitive Algorithm

We show that the best possible worst case competitive ratio of any deterministic algorithm for weighted online roommates problem is arbitrarily close to 4. This proves that the 4-competitive algorithm proposed by Bernstein and Rajagopalan [3] for the weighted version of the online roommates problem actually attains the best possible competitive ratio.

scholarly journals Risk strategy analysis for an online rental problem of durable equipment with a transaction cost

2021 ◽  
Vol 15 ◽  
pp. 174830262110084
Author(s):  
Chunlin Xin ◽  
Jianwen Zhang ◽  
Ziping Wang
Keyword(s):  
Transaction Cost ◽  
Competitive Analysis ◽  
Competitive Ratio ◽  
Risk Tolerance ◽  
Probabilistic Forecast ◽  
Case Scenario ◽  
Strategy Analysis ◽  
Worst Case ◽  
Probabilistic Forecasts ◽  
Deterministic Strategy

This study introduces the second-hand market into the famous ski-rental model, presents an online rental problem of durable equipment with a transaction cost, and designs an optimal deterministic competitive strategy. The traditional competitive analysis is based on the worst-case scenario; hence, its results are too conservative. Even though investors want to manage and control their risks in reality, in some cases, they are willing to undertake higher risk to obtain greater benefits. Considering this situation, this study designs a risk strategy combining the decision makers’ risk tolerance with certain and probabilistic forecasts. Numerical analysis shows that the proposed risk strategy can improve the competitive ratio. This study introduces the idea of risk compensation into traditional competitive analysis and designs strategies for online rental of durable equipment based on forecast. The decision maker selects a strategy according to risk tolerance and forecast. If the forecast is correct, then a reward is obtained; otherwise, the risk is guaranteed to be within the decision maker’s risk tolerance. The optimal restricted ratio, that is, the competitive ratio of a risk strategy, is less than the optimal competitive ratio of a deterministic strategy. Therefore, the performance of the proposed risk strategy is better than a deterministic strategy. At the same time, the risk strategy based on the probabilistic forecast represents an extension of the strategy based on a certain forecast. In other words, the risk strategy based on a certain forecast is a special case of the risk strategy based on the probabilistic forecast.

Unsupervised and Semi-Supervised Graph-Spectral Algorithms for Robust Extraction of Arbitrarily Shaped Fuzzy Clusters

2007 ◽  
Vol 11 (6) ◽  
pp. 554-560 ◽  
Author(s):  
Weiwei Du ◽  
◽  
Kiichi Urahama
Keyword(s):  
Image Retrieval ◽  
Directed Graphs ◽  
Noisy Data ◽  
Lagrangian Function ◽  
Color Images ◽  
Web Page ◽  
Undirected Graphs ◽  
Face Images ◽  
Spectral Algorithms ◽  
Similarity Searches

We present unsupervised and semi-supervised algorithms for extracting fuzzy clusters in weighted undirected regular, undirected bipartite, and directed graphs. We derive the semi-supervised algorithms from the Lagrangian function in unsupervised methods for extracting dominant clusters in a graph. These algorithms are robust against noisy data and extract arbitrarily shaped clusters. We demonstrate applications for similarity searches of data such as image retrieval in face images represented by undirected graphs, quantized color images represented by undirected bipartite graphs, and Web page links represented by directed graphs.

scholarly journals Solving Multi-agent Path Finding on Strongly Biconnected Digraphs

2018 ◽  
Vol 62 ◽  
pp. 273-314
Author(s):  
Adi Botea ◽  
Davide Bonusi ◽  
Pavel Surynek
Keyword(s):  
Empirical Analysis ◽  
Polynomial Time ◽  
Directed Graphs ◽  
Path Finding ◽  
Undirected Graphs ◽  
Suboptimal Solutions ◽  
Polynomial Time Algorithms ◽  
Asymmetric Communication ◽  
Multi Agent

Much of the literature on suboptimal, polynomial-time algorithms for multi-agent path finding focuses on undirected graphs, where motion is permitted in both directions along a graph edge. Despite this, traveling on directed graphs is relevant in navigation domains, such as path finding in games, and asymmetric communication networks.We consider multi-agent path finding on strongly biconnected directed graphs. We show that all instances with at least two unoccupied positions have a solution, except for a particular, degenerate subclass where the graph has a cyclic shape. We present diBOX, an algorithm for multi-agent path finding on strongly biconnected directed graphs. diBOX runs in polynomial time, computes suboptimal solutions and is complete for instances on strongly biconnected digraphs with at least two unoccupied positions. We theoretically analyze properties of the algorithm and properties of strongly biconnected directed graphs that are relevant to our approach. We perform a detailed empirical analysis of diBOX, showing a good scalability. To our knowledge, our work is the first study of multi-agent path finding focused on directed graphs.

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