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Koutsoupias, Elias; Papadimitriou, Christos H.
doi: 10.1145/210118.210128pmid: N/A
We prove that the work function algorithm for the k -server problem has a competitive ratio at most 2 k −1. Manasse et al. 1988 conjectured that the competitive ratio for the k -server problem is exactly k (it is trivially at least k ); previously the best-known upper bound was exponential in k . Our proof involves three crucial ingredients: A quasiconvexity property of work functions, a duality lemma that uses quasiconvexity to characterize the configuration that achieve maximum increase of the work function, and a potential function that exploits the duality lemma.
doi: 10.1145/210118.210130pmid: N/A
Implementation of programming language interpreters, proving theorem of the form A=B, implementation of abstract data types, and program optimization are all problems that can be reduced to the problem of finding a normal form for an expression with respect to a finite set of equations. In 1980, Chew proposed an elegant congruence closure based simplifier (CCNS) for computing with regular systems, which stores the history of it computations in a compact data structure. In 1990, Verma and Ramakrishnan showed that it can also be used for noetherian systems with no overlaps. In this paper, we develop a general theory of using CCNS for computing normal forms and present several applications. Our results are more powerful and widely applicable than earlier work. We present an independent set of postulates and prove that CCNS can be used for any system that satisfies them. (This proof is based on the notion of strong closure ). We then show that CCNS can be used for consistent convergent systems and for various kinds of priority rewrite systems. This is the first time that the applicability of CCNS has been shown for priority systems. Finally, we present a new and simpler translation scheme for converting convergent systems into effectively nonoverlapping convergent priority systems. Such a translation scheme has been proposed earlier, but we show that it is incorrect. Because CCNS requires some strong properties of the given system, our demonstration of its wide applicability is both difficult and surprising. The tension between demands imposed by CCNS and our efforts to satisfy them gives our work much general significance. Our results are partly achieved through the idea of effectively simulating “bad” systems by almost-equivalent “good” ones, partly through our theory that substantially weakens the demands, and partly through the design of a powerful and unifying reduction proof method.
Awerbuch, Baruch; Peleg, David
doi: 10.1145/210118.210132pmid: N/A
This paper deals with the problem of maintaining a distributed directory server, that enables us to keep track of mobile users in a distributed network. The paper introduces the graph-theoretic concept of regional matching , and demonstrates how finding a regional matching with certain parameters enables efficient tracking. The communication overhead of our tracking mechanism is within a polylogarithmic factor of the lower bound.
Tempero, Ewan D.; Ladner, Richard E.
doi: 10.1145/210118.210133pmid: N/A
We consider the sequence transmission problem, that is, the problem of transmitting an infinite sequence of messages x 1 x 2 x 3 … over a channel that can both lose and reorder packets. We define performance measures, ideal transmission cost and recovery cost, for protocols that solve the sequence transmission problem. Ideal transmission cost measures the number of packets needed to deliver x n when the channel is behaving ideally and recovery cost measures how long it takes, in terms of number of messages delivered, for the ideal transmission cost to take hold once the channel begins behaving ideally. We also define lookahead, which measures the number of messages the sender can be ahead of the receiver in the protocol. We show that any protocol with constant recovery cost and lookahead requires linear ideal transmission cost. We describe a protocol, P lin , that has ideal transmission cost 2 n , recovery cost 1, and lookahead 0.
doi: 10.1145/210118.210136pmid: N/A
The spectral method is the best currently known technique to prove lower bounds on expansion. Ramanujan graphs, which have asymptotically optimal second eigenvalue, are the best-known explicit expanders. The spectral method yielded a lower bound of k /4 on the expansion of linear-sized subsets of k -regular Ramanujan graphs. We improve the lower bound on the expansion of Ramanujan graphs to approximately k /2. Moreover, we construct a family of k -regular graphs with asymptotically optimal second eigenvalue and linear expansion equal to k /2. This shows that k /2 is the best bound one can obtain using the second eigenvalue method. We also show an upper bound of roughly 1+ k-1 on the average degree of linear-sized induced subgraphs of Ramanujan graphs. This compares positively with the classical bound 2 k-1 . As a byproduct, we obtain improved results on random walks on expanders and construct selection networks (respectively, extrovert graphs) of smaller size (respectively, degree) than was previously known.
Conforti, Michele; Cornuéjols, Gérard
doi: 10.1145/210118.210137pmid: N/A
In propositional logic, several problems, such as satisfiability, MAX SAT and logical inference, can be formulated as integer programs. In this paper, we consider sets of clauses for which the corresponding integer programs can be solved as linear programs. We prove that balanced sets of clauses have this property.
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