Smooth Scheduling under Variable Rates or the Analog-Digital Confinement Game

This work considers non-terminating scheduling problems in which a system of multiple resources serves clients having variable needs. The system has m identical resources and n clients; in each time slot each resource may serve at most one client; in each such slot t each client γ has a rate, a real number ρ _γ (t), that specifies his needs in this slot. The rates satisfy the restriction ∑ _γ ρ _γ (t)≤m for any slot t. Except of this restriction, the rates can vary in arbitrary fashion. (This contrasts most prior works in this area in which the rates of the clients are constant.) The schedule is required to be smooth as follows: a schedule is Δ -smooth if for all time intervals I the absolute difference between the amount of service received by each client γ to his nominal needs of ∑ _t∈I ρ _γ (t) is less than Δ. Our objective are online schedulers that produce Δ-smooth schedules where Δ is a small constant which is independent of m and n. Our paper constructs such schedulers; these are the first online Δ-smooth schedulers, with a constant Δ, for clients with arbitrarily variable rates in a single or multiple resource system. Furthermore, the paper also considers a non-concurrent environment in which there is an additional restriction that each client is served at most once in each time slot; it presents the first online smooth schedulers for variable rates under this restriction. The above non-concurrent restriction is crucial in some applications (e.g., CPU scheduling). It has been pointed out that this restriction “adds a surprising amount of difficulty” to the scheduling problem. However, this observation was never formalized and, of course, was never proved. Our paper formalizes and proves some aspects of this observation. Another contribution of this paper is the introduction of a complete information, two player game called the analog-digital confinement game. In such a game pebbles are located on the real line; the two players, the analog player and the digital player, take alternating turns and each one, in his turn, moves some of the pebbles; the digital player moves the pebbles backwards by discrete distances while the analog player moves the pebbles forward by analog distances; the aim of the analog player is to cause one pebble (or more) to escape a pre-defined real interval while the aim of the digital player is to confine the pebbles into the interval. We demonstrate that this game is a convenient framework to study the general question of how to approximate an analog process by a digital one. All the above scheduling results are established via this game. In this derivation, the pebbles represent the clients, the analog player generates the needs of the clients and the digital player generates the schedule. Dedicated to the memory of Professor Shimon Even for his inspiration and encouragement     

Degree-Optimal Routing for P2P Systems

We define a family of Distributed Hash Table systems whose aim is to combine the routing efficiency of randomized networks—e.g. optimal average path length O(log ² n/δlog δ) with δ degree—with the programmability and startup efficiency of a uniform overlay—that is, a deterministic system in which the overlay network is transitive and greedy routing is optimal. It is known that Ω(log n) is a lower bound on the average path length for uniform overlays with O(log n) degree (Xu et al., IEEE J. Sel. Areas Commun. 22(1), 151–163, 2004). Our work is inspired by neighbor-of-neighbor (NoN) routing, a recently introduced variation of greedy routing that allows us to achieve optimal average path length in randomized networks. The advantage of our proposal is that of allowing the NoN technique to be implemented without adding any overhead to the corresponding deterministic network. We propose a family of networks parameterized with a positive integer c which measures the amount of randomness that is used. By varying the value c, the system goes from the deterministic case (c=1) to an “almost uniform” system. Increasing c to relatively low values allows for routing with asymptotically optimal average path length while retaining most of the advantages of a uniform system, such as easy programmability and quick bootstrap of the nodes entering the system. We also provide a matching lower bound for the average path length of the routing schemes for any c. This work was partially supported by the Italian FIRB project “WEB-MINDS” (Wide-scalE, Broadband MIddleware for Network Distributed Services), .     

A Randomized Algorithm for Online Unit Clustering

In this paper, we consider the online version of the following problem: partition a set of input points into subsets, each enclosable by a unit ball, so as to minimize the number of subsets used. In the one-dimensional case, we show that surprisingly the naïve upper bound of 2 on the competitive ratio can be beaten: we present a new randomized 15/8-competitive online algorithm. We also provide some lower bounds and an extension to higher dimensions.     

On the Black-Box Complexity of Sperner’s Lemma

We present several results on the complexity of various forms of Sperner’s Lemma in the black-box model of computing. We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension. The query complexity of our algorithm is linear in the separation number of the skeleton graph of the manifold and the size of its boundary. As a corollary we get an deterministic query algorithm for the black-box version of the problem 2D-SPERNER, a well studied member of Papadimitriou’s complexity class PPAD. This upper bound matches the deterministic lower bound of Crescenzi and Silvestri. The tightness of this bound was not known before. In another result we prove for the same problem an lower bound for its probabilistic, and an lower bound for its quantum query complexity, showing that all these measures are polynomially related. Research supported by the European Commission IST Integrated Project Qubit Application (QAP) 015848, the OTKA grants T42559 and T46234, and by the ANR Blanc AlgoQP grant of the French Research Ministry.     

Cryptographic and Physical Zero-Knowledge Proof Systems for Solutions of Sudoku Puzzles

We consider cryptographic and physical zero-knowledge proof schemes for Sudoku, a popular combinatorial puzzle. We discuss methods that allow one party, the prover, to convince another party, the verifier, that the prover has solved a Sudoku puzzle, without revealing the solution to the verifier. The question of interest is how a prover can show: (i) that there is a solution to the given puzzle, and (ii) that he knows the solution, while not giving away any information about the solution to the verifier. In this paper we consider several protocols that achieve these goals. Broadly speaking, the protocols are either cryptographic or physical. By a cryptographic protocol we mean one in the usual model found in the foundations of cryptography literature. In this model, two machines exchange messages, and the security of the protocol relies on computational hardness. By a physical protocol we mean one that is implementable by humans using common objects, and preferably without the aid of computers. In particular, our physical protocols utilize items such as scratch-off cards, similar to those used in lotteries, or even just simple playing cards. The cryptographic protocols are direct and efficient, and do not involve a reduction to other problems. The physical protocols are meant to be understood by “lay-people” and implementable without the use of computers. Research of R. Gradwohl was supported by US-Israel Binational Science Foundation Grant 2002246. Research of M. Naor was supported in part by a grant from the Israel Science Foundation. Research of B. Pinkas was supported in part by the Israel Science Foundation (grant number 860/06). Research of G.N. Rothblum was supported by NSF grant CNS-0430450 and NSF grant CFF-0635297.     

Classification of semantic relations between nominals

The NLP community has shown a renewed interest in deeper semantic analyses, among them automatic recognition of semantic relations in text. We present the development and evaluation of a semantic analysis task: automatic recognition of relations between pairs of nominals in a sentence. The task was part of SemEval-2007, the fourth edition of the semantic evaluation event previously known as SensEval. Apart from the observations we have made, the long-lasting effect of this task may be a framework for comparing approaches to the task. We introduce the problem of recognizing relations between nominals, and in particular the process of drafting and refining the definitions of the semantic relations. We show how we created the training and test data, list and briefly describe the 15 participating systems, discuss the results, and conclude with the lessons learned in the course of this exercise.     

A cost-effective lexical acquisition process for large-scale thesaurus translation

Thesauri and controlled vocabularies facilitate access to digital collections by explicitly representing the underlying principles of organization. Translation of such resources into multiple languages is an important component for providing multilingual access. However, the specificity of vocabulary terms in most thesauri precludes fully-automatic translation using general-domain lexical resources. In this paper, we present an efficient process for leveraging human translations to construct domain-specific lexical resources. This process is illustrated on a thesaurus of 56,000 concepts used to catalog a large archive of oral histories. We elicited human translations on a small subset of concepts, induced a probabilistic phrase dictionary from these translations, and used the resulting resource to automatically translate the rest of the thesaurus. Two separate evaluations demonstrate the acceptability of the automatic translations and the cost-effectiveness of our approach.

DanNet: the challenge of compiling a wordnet for Danish by reusing a monolingual dictionary

This paper is a contribution to the discussion on compiling computational lexical resources from conventional dictionaries. It describes the theoretical as well as practical problems that are encountered when reusing a conventional dictionary for compiling a lexical-semantic resource in terms of a wordnet. More specifically, it describes the methodological issues of compiling a wordnet for Danish, DanNet, from a monolingual basis, and not—as is often seen—by applying the translational expansion method with Princeton WordNet as the English source. Thus, we apply as our basis a large, corpus-based printed dictionary of modern Danish. Using this approach, we discuss the issues of readjusting inconsistent and/or underspecified hyponymy hierarchies taken from the conventional dictionary, sense distinctions as opposed to the synonym sets of wordnets, generating semantic wordnet relations on the basis of sense definitions, and finally, supplementing missing or implicit information.     

Computer-Forensik in der Praxis

Zusammenfassung  Im Zeitalter der Informationstechnologie und der umfassenden Vernetzung vieler Systeme ben?tigt ein Dieb weder eine Brechstange noch muss er im Schutze der Dunkelheit vorgehen. Vielmehr kann er über das Internet, oder lokale Netzwerke, kommen und gehen wann er will, ohne sich der Gefahr einer Entdeckung und Verhaftung auszusetzen. In vielen F?llen ist ein solcher Einbrecher l?ngst über alle Berge, bevor seine Tat überhaupt bemerkt wird. Trotzdem hinterl?sst er Spuren — deren Aufspürung und Analyse die Aufgabe des Computer-Forensikers ist. Zur Unterstützung dieser Arbeit existiert eine Vielzahl an Open-Source-Werkzeugen, die es durchaus mit ihrer kommerziellen Konkurrenz aufnehmen k?nnen.