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Content delivery networks that distribute much of the world's content and services solve this large and complex stable marriage problem between users and servers every tens of seconds to enable billions of users to be matched up with their respective servers that can provide the requested web pages, videos, or other services. In , David Gale and Lloyd Shapley proved that, for any equal number of men and women, it is always possible to solve the SMP and make all marriages stable.

They presented an algorithm to do so. The Gale—Shapley algorithm involves a number of "rounds" or " iterations ":. While the solution is stable, it is not necessarily optimal from all individuals' points of view. The traditional form of the algorithm is optimal for the initiator of the proposals and the stable, suitor-optimal solution may or may not be optimal for the reviewer of the proposals. An example is as follows:. All three are stable because instability requires one of the participants to be happier with an alternative match.

Giving one group their first choices ensures that the matches are stable because they would be unhappy with any other proposed match. Giving everyone their second choice ensures that any other match would be disliked by one of the parties. The algorithm converges in a single round on the suitor-optimal solution because each reviewer receives exactly one proposal, and therefore selects that proposal as its best choice, ensuring that each suitor has an accepted offer, ending the match. This asymmetry of optimality is driven by the fact that the suitors have the entire set to choose from, but reviewers choose between a limited subset of the suitors at any one time.

In the classical version of the problem, each person must rank the members of the opposite sex in strict order of preference. However, in a real-world setting, a person may prefer two or more persons as equally favorable partner. Such tied preference is termed as indifference. If tied preference lists are allowed then the stable marriage problem will have three notions of stability which are discussed in the below sections.

Ties in men and women's preference list are broken arbitrarily. Preference lists are reduced as algorithm proceeds. Below is the pseudo-code. Irving [7] has provided the algorithm which checks if such strongly stable matching exists and outputs the matching if it exists. The algorithm computes perfect matching between sets of men and women, thus finding the critical set of men who are engaged to multiple women. Since such engagements are never stable, all such pairs are deleted and the proposal sequence will be repeated again until either 1 some man's preference list becomes empty in which case no strongly stable matching exists or 2 strongly stable matching is obtained.

Book file PDF easily for everyone and every device. However, this algorithm relies upon exponential weights which, when used in practice, may result in overflows or memory issues. In this talk I describe a new polynomial-time algorithm to compute a rank-maximal stable matching using a combinatorial approach, without the need to revert to exponential weights.

The talk is based on joint work with David Manlove. This classical model assumes that preference lists are strictly ordered. In this context, what we seek is a stable matching of students to projects. However, when the preference lists involve ties, three different stability concepts naturally arise; namely, weak stability, strong stability and super-stability. Further, I will describe a polynomial-time algorithm to find a strongly stable matching or to report that no such matching exists, given an instance of SPA-ST.

Network Tomography is a family of distributed failure detection algorithms based on the spreading of end-to-end measurements [1,7] along the network edges. We study the identifiability of simultaneous node failures in Line-of-Sight LoS for short networks.

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LoS networks were introduced by Frieze et al. But LoS networks generalize grids in that edges are allowed between nodes that are not necessarily next to each other in the network embedding.

The main contribution of our work is the analysis of a strategy to identify large sets of simultaneously failing nodes in LoS networks. Coates, A. Hero, R. Nowak, and B. Internet tomography.

Network tomography of binary network performance characteristics. Frieze, J. Kleinberg, R. Ravi, and W.

ISBN 13: 9789814425247

Line-of-sight networks. In Proc. Galesi and F. Tight bounds for maximal identifiability of failure nodes in boolean network tomography. Ghita, C.

[PDF] Parallel algorithms for matching under preference - Semantic Scholar

Karakus, K. Argyraki, and P. Shifting network tomography toward a practical goal. Ma, T. He, A. Swami, D.

Algorithmics Of Matching Under Preferences : David Manlove :

Towsley, and K. Network capability in localizing node failures via end-to-end path measurements. Network tomography: Estimating source-destination traffic intensities from link data. Journal of the American Statistical Association , 91 , This approach has proven to be highly successful in delineating our understanding of NP-hard problems.

First attempts in this direction have considered a few individual problems, with some success: Fafianie and Kratsch [MFCS'14] and Chitnis et al. In this work, we initiate a systematic study of graph problems from the paradigm of parameterized streaming algorithms. On the algorithmic side, our parameterized streaming algorithms use techniques from the FPT world such as bidimensionality, iterative compression and bounded-depth search trees.

On the hardness side, we obtain lower bounds for the parameterized streaming complexity of various problems via novel reductions from problems in communication complexity. We also show how conditional lower bounds for kernels and W-hard problems translate to lower bounds for parameterized streaming algorithms.

Random Access Machine - Intro to Theoretical Computer Science

It is our hope that this work on parameterized streaming algorithms leads to two-way flow of ideas between these two previously separated areas of theoretical computer science. In computer science this is known as the Curry-Howard correspondence which identifies the typed lambda-calculus both as a notation system for proofs and a programming language. A related - and regarding specification more expressive - correspondence between proofs and programs is provided by Kleene's realizability which can be viewed as a computationally enriched semantics of logic and arithmetic.

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Kleene proved the fundamental Soundness Theorem which shows that from a constructive proof of a formula one can extract an algorithm that realizes the proven formula, that is, solves the computational problem it expresses. Realizability offers an attractive alternative to program verification: Instead of first writing a program and then trying to prove that it meets its specification, one first proves that the specification is satisfiable and then extracts a program provably satisfying it.

The advantages of program extraction over verification are obvious: While it is in general undecidable whether or not a program meets its specification, the correctness of a proof can be easily checked. Hence program extraction not only yields correct programs but also provides formal correctness proofs for free. Despite the virtues of program extraction, the currently dominating technologies for producing formally certified software are based on traditional 'programming-first' methodologies such as model-checking and formal verification. The main reasons are that program extraction is considered too restricted, since it covers only functional programming but misses out on many other computational paradigms, and too complicated and demanding for software developers to be of practical relevance.

This talk will present a logical system IFP Intuitionistic Fixed point Logic as a basis for program extraction that addresses these issues. After a brief introduction to IFP an overview of the main case studies - most of them implemented in the Minlog proof system - is given. This is followed by an outline of new developments aiming to extend program extraction to capture non-functional computational paradigms such as concurrency and state based computation.

For each request and without knowledge of future requests, the algorithm has to select a taxi to transport the passenger.

Research interests

The goal is to minimize the total distance traveled by all taxis. The talk will focus mostly on the hard version, which is substantially more difficult. I will also describe the main ideas of an algorithm based on growing, shrinking and shifting regions which achieves a constant competitive ratio for three taxis on the line abstracting the scheduling of three elevators.

The talk is based on joint work with Elias Koutsoupias Coester and Koutsoupias. To appear. Each packet has a deadline, representing its urgency, and a non-negative weight, that represents its priority. Only one packet can be transmitted in any time slot, so, if the system is overloaded, some packets will inevitably miss their deadlines and be dropped.

Algorithmics Of Matching Under Preferences by David Manlove (Hardback, 2013)

In this scenario, the natural objective is to compute a transmission schedule that maximizes the total weight of packets which are successfully transmitted. The problem is inherently online, with the scheduling decisions made without the knowledge of future packet arrivals. The goal is to develop an algorithm with the lowest possible competitive ratio, which is the worst-case ratio between the optimum total weight of a schedule computed by an offline algorithm and the weight of a schedule computed by a deterministic online algorithm.

We then outline main ideas of its analysis and discuss possible extensions of this work. The demand of fully automatic operation puts forward higher requirements for the precise control of railway signalling systems. Conventional over-speed protection methods monitor the speed at discrete time instants.