734 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    On linear, fractional, and submodular optimization

    Get PDF
    In this thesis, we study four fundamental problems in the theory of optimization. 1. In fractional optimization, we are interested in minimizing a ratio of two functions over some domain. A well-known technique for solving this problem is the Newton– Dinkelbach method. We propose an accelerated version of this classical method and give a new analysis using the Bregman divergence. We show how it leads to improved or simplified results in three application areas. 2. The diameter of a polyhedron is the maximum length of a shortest path between any two vertices. The circuit diameter is a relaxation of this notion, whereby shortest paths are not restricted to edges of the polyhedron. For a polyhedron in standard equality form with constraint matrix A, we prove an upper bound on the circuit diameter that is quadratic in the rank of A and logarithmic in the circuit imbalance measure of A. We also give circuit augmentation algorithms for linear programming with similar iteration complexity. 3. The correlation gap of a set function is the ratio between its multilinear and concave extensions. We present improved lower bounds on the correlation gap of a matroid rank function, parametrized by the rank and girth of the matroid. We also prove that for a weighted matroid rank function, the worst correlation gap is achieved with uniform weights. Such improved lower bounds have direct applications in submodular maximization and mechanism design. 4. The last part of this thesis concerns parity games, a problem intimately related to linear programming. A parity game is an infinite-duration game between two players on a graph. The problem of deciding the winner lies in NP and co-NP, with no known polynomial algorithm to date. Many of the fastest (quasi-polynomial) algorithms have been unified via the concept of a universal tree. We propose a strategy iteration framework which can be applied on any universal tree

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Rhoda: ‘Comrade Kadalie, You Are Out of Order!

    Get PDF
    This authorized biography was made possible through the gracious help of my mother-in-law, Rhoda Kadalie, who provided generous access to her files, letters, photographs, and extensive library of documents. She made time to sit with me for several hours of interviews from September through October 2021, to answer questions as they arose, and to offer innumerable clarifications. Rhoda also reviewed the first draft of the biography in December 2021, making corrections and additions, and contributing some of her own original vignettes, never before published

    Improved Learning-Augmented Algorithms for the Multi-Option Ski Rental Problem via Best-Possible Competitive Analysis

    Full text link
    In this paper, we present improved learning-augmented algorithms for the multi-option ski rental problem. Learning-augmented algorithms take ML predictions as an added part of the input and incorporates these predictions in solving the given problem. Due to their unique strength that combines the power of ML predictions with rigorous performance guarantees, they have been extensively studied in the context of online optimization problems. Even though ski rental problems are one of the canonical problems in the field of online optimization, only deterministic algorithms were previously known for multi-option ski rental, with or without learning augmentation. We present the first randomized learning-augmented algorithm for this problem, surpassing previous performance guarantees given by deterministic algorithms. Our learning-augmented algorithm is based on a new, provably best-possible randomized competitive algorithm for the problem. Our results are further complemented by lower bounds for deterministic and randomized algorithms, and computational experiments evaluating our algorithms' performance improvements.Comment: 23 pages, 1 figur

    The Protection of Brands against Unfair Competition: A proposal for reform

    Get PDF
    It is an established marketplace reality that the success of a brand attracts competitors who may wish to follow its path or attempt to utilise its success for their own commercial gain. One such case is the launch of a lower price L’Oréal smell-alike perfume by Bellure in 2006. A mimicking of one or several features of a brand is aimed at changing the relevant consumer’s purchase decision by giving ‘a wink of an eye to existing branded product’ which can be more effective than launching a distinctively new product. A competition as such, that serves to reduce prices and increase consumers’ choice with no likelihood of confusion, is considered to be in the wider interest of the public in the current English Law. Pursuant to this view, protection to brands against unfair competition by mere misappropriation is not acknowledged by the English law. This lack of acknowledgement leads to insufficient protection to brands in the marketplace against rivalry which in turn undermine the intellectual flourishing in society – a vital part of humans’ nature. This thesis argues that the inclusion of brands in a broader scope of protection against unfair competition by misappropriation in the English law serves to enhance the intellectual flourishing of society. It therefore suggests that limitations to certain un-authorised uses of brands in the course of trade now needs to be acknowledged. For that purpose, Part 1 of this thesis offers a critical analysis to the current English approach towards the protection of brands against unfair competition misappropriation (in particular, under the tort of passing off and section 10 of the TMA 1994) and demonstrates how it is designed by, and limited to, economic rationality while overlooking brands in their wider sense. Part 2 utilises the non-economic framework of intellectual flourishing, as an obligation on society, to provide a broad view on the complex nature of brands and the implications of their protection (or lack thereof) upon society. The analysis in this thesis results in the proposal of a statutory clause that replaces the present section 10(3) of the TMA 1994, as well as the implementation of statutory defences into section 11 of the TMA 1994. Rather than broadening private rights in the marketplace, the ultimate goal of the proposed protection alongside the counterbalancing defences is to contribute towards meeting the larger obligation on society to flourish intellectually. In particular, to encourage individuals to use their senses and engage their imagination to create further knowledge in society, to participate in meaning-making and communicate through an enhanced semiotic discourse and to exercise new modes of thinking by amending and altering existing meanings through an enhanced memetic discourse. Without having adequate protection of brands against unfair competition by misappropriation in the marketplace, the ability to utilise the above-mentioned outcomes of those intellectual values is undermined

    Online Dynamic Acknowledgement with Learned Predictions

    Full text link
    We revisit the online dynamic acknowledgment problem. In the problem, a sequence of requests arrive over time to be acknowledged, and all outstanding requests can be satisfied simultaneously by one acknowledgement. The goal of the problem is to minimize the total request delay plus acknowledgement cost. This elegant model studies the trade-off between acknowledgement cost and waiting experienced by requests. The problem has been well studied and the tight competitive ratios have been determined. For this well-studied problem, we focus on how to effectively use machine-learned predictions to have better performance. We develop algorithms that perform arbitrarily close to the optimum with accurate predictions while concurrently having the guarantees arbitrarily close to what the best online algorithms can offer without access to predictions, thereby achieving simultaneous optimum consistency and robustness. This new result is enabled by our novel prediction error measure. No error measure was defined for the problem prior to our work, and natural measures failed due to the challenge that requests with different arrival times have different effects on the objective. We hope our ideas can be used for other online problems with temporal aspects that have been resisting proper error measures.Comment: To appear in INFOCOM 202

    Spatial and temporal hierarchical decomposition methods for the optimal power flow problem

    Get PDF
    The subject of this thesis is the development of spatial and temporal decomposition methods for the optimal power flow problem, such as in the transmissiondistribution network topologies. In this context, we propose novel decomposition interfaces and effectivemethodology for both the spatial and temporal dimensions applicable to linear and non-linear representations of the OPF problem. These two decomposition strategies are combined with a Benders-based algorithmand have advantages in model building time, memory management and solving time. For example, in the 2880-period linear problems, the decomposition finds optimal solutions up to 50 times faster and allows even larger instances to be solved; and in multi-period non-linear problems with 48 periods, close-to-optimal feasible solutions are found 7 times faster. With these decompositions, detailed networks can be optimized in coordination, effectively exploiting the value of the time-linked elements in both transmission and distribution levels while speeding up the solution process, preserving privacy, and adding flexibility when dealing with different models at each level. In the non-linear methodology, significant challenges, such as active set determination, instability and non-convex overestimations, may hinder its effectiveness, and they are addressed, making the proposed methodology more robust and stable. A test network was constructed by combining standard publicly available networks resulting in nearly 1000 buses and lines with up to 8760 connected periods; several interfaces were presented depending on the problemtype and its topology using a modified Benders algorithm. Insight was given into why a Benders-based decomposition was used for this type of problem instead of a common alternative: ADMM. The methodology is useful mainly in two sets of applications: when highly detailed long-termlinear operational problems need to be solved, such as in planning frameworks where the operational problems solved assume no prior knowledge; and in full AC-OPF problems where prior information from historic solutions can be used to speed up convergence

    LIPIcs, Volume 274, ESA 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 274, ESA 2023, Complete Volum
    • …
    corecore