Dynamic pricing of servers on trees

In this paper we consider the k-server problem where events are generated by selfish agents, known as the selfish k-server problem. In this setting, there is a set of k servers located in some metric space. Selfish agents arrive in an online fashion, each has a request located on some point in the metric space, and seeks to serve his request with the server of minimum distance to the request. If agents choose to serve their request with the nearest server, this mimics the greedy algorithm which has an unbounded competitive ratio. We propose an algorithm that associates a surcharge with each server independently of the agent to arrive (and therefore, yields a truthful online mechanism). An agent chooses to serve his request with the server that minimizes the distance to the request plus the associated surcharge to the server. This paper extends [9], which gave an optimal k-competitive dynamic pricing scheme for the selfish k-server problem on the line. We give a k-competitive dynamic pricing algorithm for the selfish k-server problem on tree metric spaces, which matches the optimal online (non truthful) algorithm. We show that an α-competitive dynamic pricing scheme exists on the tree if and only if there exists α-competitive online algorithm on the tree that is lazy and monotone. Given this characterization, the main technical difficulty is coming up with such an online algorithm

Competitive Paging Algorithms

The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. We develop the marking algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor of 2Hk of optimum. (Where Hk is the kth harmonic number, which is roughly In k.) The best such factor that can be achieved is Hk. This is in contrast to deterministic algorithms, which cannot be guaranteed to be within a factor smaller than k of optimum. An alternative to comparing an on-line algorithm with the optimum off-line algorithm is the idea of comparing it to several other on-line algorithms. We have obtained results along these lines for the paging problem. Given a set of on-line algorithms and a se

Green Paging and Parallel Paging

We study two fundamental variants of the classic paging problem: green paging and parallel paging. In green paging one can choose the exact memory capacity in use at any given instant, between a maximum of k and a minimum of k/p pages; the goal is to minimize the integral of this number over the time required to complete a computation (note that running at lower capacity is not necessarily better, since might disproportionately increase the total completion time). In parallel paging, a memory of k pages is shared between p processors, each carrying out a separate computation; the goal is to minimize the respective completion times. We show how these two different problems are strictly related: any efficient solution to green paging can be converted into an efficient solution to parallel paging, and any lower bound for green paging can be converted into a lower bound for parallel paging - -in both cases in a black-box fashion. Exploiting this relation, we provide tight upper and lower bounds of (log p) on the competitive ratio with O(1) resource augmentation for both problems

Competitive Generalized Auctions

We describe mechanisms for auctions that are simultaneously truthful (alternately known as strategy-proof or incentive-compatible) and guarantee high "net" profit. We make use of appropriate variants of competitive analysis of algorithms in designing and analyzing our mechanisms. Thus, we do not require any probabilistic assumptions on bids. We presen

Competitive Paging Algorithms

The paging problem is that of deciding which pages to keep in a memory of k pages in order to minimize the number of page faults. We develop the marking algorithm, a randomized on-line algorithm for the paging problem. We prove that its expected cost on any sequence of requests is within a factor of 2Hk of optimum. (Where Hk is the kth harmonic number, which is roughly Ink.) The best such factor that can be achieved is Hk. This is in contrast to deterministic algorithms, which cannot be guaranteed to be within a factor smaller than k of optimum. An alternative to comparing an on-line algorithm with the optimum off-line algorithm is the idea of comparing it to several other on-line algorithms. We have obtained results along these lines for the paging problem. Given a set of on-line algorithm

Verified Verifiers for Verifying Elections

The security and trustworthiness of elections is critical to democracy; alas, securing elections is notoriously hard. Powerful cryptographic techniques for verifying the integrity of electronic voting have been developed and are in increasingly common use. The claimed security guarantees of most of these techniques have been formally proved. However, implementing the cryptographic verifiers which utilize these techniques is a technical and error prone process, and often leads to critical errors appearing in the gap between the implementation and the formally verified design. We significantly reduce the gap between theory and practice by using machine checked proofs coupled with code extraction to produce cryptographic verifiers that are themselves formally verified. We demonstrate the feasibility of our technique by producing a formally verified verifier which we use to check the 2018 International Association for Cryptologic Research (IACR) directors election