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Determinant algorithms for random planar structures
 In Proc. of the Eighth Annual ACMSIAM Symposium on Discrete Algorithms
, 1997
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Improving a Family of Approximation Algorithms to Edge Color Multigraphs
, 1998
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The complexity of approximation PSPACEcomplete problems for hierarchical specifications
 Nordic Journal of Computing
, 1994
"... We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specied graphs, many of which are PSPACEcomplete. Assuming P 6 = PSPACE, the existence or nonexistence of such ecient approximation algorithms is characterized, for several standard graph the ..."
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Cited by 9 (4 self)
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We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specied graphs, many of which are PSPACEcomplete. Assuming P 6 = PSPACE, the existence or nonexistence of such ecient approximation algorithms is characterized, for several standard graph theoretic and combinatorial problems. We present polynomial time approximation algorithms for several standard PSPACEhard problems considered in the literature. In contrast, we show that unless P = PSPACE, there is no polynomial time approximation for any > 0, for several other problems, when the instances are specied hierarchically. We present polynomial time approximation algorithms for the following problems when the graphs are specied hierarchically: minimum vertex cover, maximum 3SAT, weighted max cut, minimum maximal matching, and bounded degree maximum independent set. In contrast, we show that unless P = PSPACE, there is no polynomial time approximation for any > 0, for the following problems when the instances are specied hierarchically: the number of true gates in a monotone acyclic circuit when all input values are specied and the optimal value of the objective function of a linear program. It is also shown that unless P = PSPACE, a performance guarantee of less than 2 cannot be obtained in polynomial time for the following problems when the instances are specied hierarchically: high degree subgraph, kvertex connected subgraph and kedge connected subgraph.
A SelfStabilizing Algorithm for Maximum Matching in Trees
, 1994
"... Constructing a maximum matching is an important problem in graph theory with applications to problems such as job assignment and task scheduling. Many efficient sequential and parallel algorithms exist for solving the problem. However, no distributed algorithms are known. In this paper, we present a ..."
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Constructing a maximum matching is an important problem in graph theory with applications to problems such as job assignment and task scheduling. Many efficient sequential and parallel algorithms exist for solving the problem. However, no distributed algorithms are known. In this paper, we present a distributed, selfstabilizing algorithm for finding a maximum matching in trees. Since our algorithm is selfstabilizing, it does not require any initialization and is tolerant to transient faults. The algorithm can also dynamically adapt to arbitrary changes in the topology of the tree. Keywords: Distributed algorithms, Matching, Selfstabilization, Trees. 1 Introduction Let G = (V; E) be an undirected graph. Two edges in E are said to be adjacent if they share a common endpoint. A matching in G is a set of edges M ` E such that no two edges in M are adjacent. A matching M is called a maximum cardinality matching, or maximum matching in short, if M has largest cardinality among all pos...
Simple Competitive Request Scheduling Strategies
 in 11th ACM Symposium on Parallel Architectures and Algorithms
, 1999
"... In this paper we study the problem of scheduling realtime requests in distributed data servers. We assume the time to be divided into time steps of equal length called rounds. During every round a set of requests arrives at the system, and every resource is able to fulfill one request per round. Ev ..."
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In this paper we study the problem of scheduling realtime requests in distributed data servers. We assume the time to be divided into time steps of equal length called rounds. During every round a set of requests arrives at the system, and every resource is able to fulfill one request per round. Every request specifies two (distinct) resources and requires to get access to one of them. Furthermore, every request has a deadline of d, i.e. a request that arrives in round t has to be fulfilled during round t +d 1 at the latest. The number of requests which arrive during some round and the two alternative resources of every request are selected by an adversary. The goal is to maximize the number of requests that are fulfilled before their deadlines expire. We examine the scheduling problem in an online setting, i.e. new requests continuously arrive at the system, and we have to determine online an assignment of the requests to the resources in such a way that every resource has to fulfil...
Nordic Journal of Computing 1(1994), 275{316. THE COMPLEXITY OF APPROXIMATING PSPACECOMPLETE PROBLEMS FOR HIERARCHICAL SPECIFICATIONS ;y
"... Abstract. We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specied graphs, many of which are PSPACEcomplete. We present polynomial time approximation algorithms for several standard PSPACEhard problems considered in the literature. In contr ..."
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Abstract. We extend the concept of polynomial time approximation algorithms to apply to problems for hierarchically specied graphs, many of which are PSPACEcomplete. We present polynomial time approximation algorithms for several standard PSPACEhard problems considered in the literature. In contrast, we prove that nding approximations for any > 0, for several other problems when the instances are specied hierarchically, is PSPACEhard. We present polynomial time approximation algorithms for the following problems when the graphs are specied hierarchically: minimum vertex cover, maximum 3SAT, weighted max cut, minimum maximal matching, and bounded degree maximum independent set. In contrast, we show that for any > 0, obtaining approximations for the following problems when the instances are specied hierarchically is PSPACEhard: the number of true gates in a monotone acyclic circuit when all input values are speci ed and the optimal value of the objective function of a linear program. It is also shown that obtaining a performance guarantee of less than 2 is PSPACEhard for the following problems when the instances are specied hierarchically: high degree subgraph, kvertex connected subgraph and kedge connected subgraph. Key words: hierarchical specications, approximation algorithms, computational complexity, algorithms and data structures 1.