Daniel Rosenkrantz | SUNY: University at Albany (original) (raw)

Papers by Daniel Rosenkrantz

Research paper thumbnail of Facility Dispersion Problems: Heuristics and Special Cases (Extended Abstract)

Workshop on Algorithms and Data Structures, 1991

ABSTRACT Facility dispersion problem deals with the location of facilities on a network so as to ... more ABSTRACT Facility dispersion problem deals with the location of facilities on a network so as to maximize some function of the distances between facilities. We consider the problem under two different optimality criteria, namely maximizing the minimum distance (MAX-MIN) between any pair of facilities and maximizing the average distance (MAX-AVG) between any pair of facilities. Under either criterion, the problem is known to be NP-hard, even when the distances satisfy the triangle inequality. We consider the question of obtaining near-optimal solutions. For the MAX-MIN criterion, we show that if the distances do not satisfy the triangle inequality, there is no polynomial time relative approximation algorithm unless P=NP. When the distances do satisfy the triangle inequality, we present an efficient heuristic which provides a performance guarantee of 2, thus improving the performance guarantee of 3 proven in [Wh91]. We also prove that obtaining a performance guarantee of less than 2 is NP-hard. For the MAX-AVG criterion, we present a heuristic which provides a performance guarantee of 4, provided that the distances satisfy the triangle inequality. For the 1-dimensional dispersion problem, we provide polynomial time algorithms for obtaining optimal solutions under both MAX-MIN and MAX-AVG criteria. Using the latter algorithm, we obtain a heuristic which provides a performance guarantee of 4( Ö2 - 1\sqrt 2 - 1 ) 1.657 for the 2-dimensional dispersion problem under the MAX-AVG criterion.

Research paper thumbnail of On Materializations of Array-Valued Temporaries

Lecture Notes in Computer Science, 2001

We present results demonstrating the usefulness of monolithic program analysis and optimization p... more We present results demonstrating the usefulness of monolithic program analysis and optimization prior to scalarization. In particular, models are developed for studying nonmaterialization in basic blocks consisting ofa sequence of assignment statements involving array- valued variables. We use these models to analyze the problem ofmi nimizing the number ofmat erializations in a basic block, and to develop an efficient algorithm for minimizing the number of materializations in certain cases.

Research paper thumbnail of Distributed database concurrency controls using before-values

Proceedings of the 1981 ACM SIGMOD international conference on Management of data - SIGMOD '81, 1981

Associated with the write of a database entity is both the &a... more Associated with the write of a database entity is both the "before" or old value, and the "after" or new value. Concurrency can be increased by allowing other transactions to read the before values of a given transaction. The ramifications of allowing this, particularly on a distributed system in which limited communications is desirable, are investigated. A careful distinction is

Research paper thumbnail of Sequential dynamical systems with threshold functions

A sequential dynamical system (SDS) (see [BH+01] and the references therein) consists of an undir... more A sequential dynamical system (SDS) (see [BH+01] and the references therein) consists of an undirected graph G(V,E) where each node V is associated with a Boolean state (s{sub }) and a symmetric Boolean function f{sub } (called the local transition function at ). The inputs to f{sub } are s{sub } and the states of all the nodes adjacent to . In each step of the SDS, the nodes update their state values using their local transition functions in the order specified by a given permutation of the nodes. A configuration of the SDS is an n-tuple (b, b...,b{sub n}) where n = |V| and b{sub i} {l_brace}0,1{r_brace} is the state value of node {sub i}. The system starts in a specified initial configuration and each step of the SDS produces a (possibly new) configuration.

Research paper thumbnail of Segmentation of Time Series Data

Segmentation of Time Series Data (9781605660103): Parvathi Chundi, Daniel J. Rosenkrantz: Book Ch... more Segmentation of Time Series Data (9781605660103): Parvathi Chundi, Daniel J. Rosenkrantz: Book Chapters.

Research paper thumbnail of Predecessor and Permutation Existence Problems for Sequential Dynamical Systems

A class of finite discrete dynamical systems, called Sequential Dynamical Systems (SDSs), was int... more A class of finite discrete dynamical systems, called Sequential Dynamical Systems (SDSs), was introduced in BMR99, BR991 as a formal model for analyzing simulation systems. An SDS S is a triple (G, F,n ),w here (i) G(V,E ) is an undirected graph with n nodes with each node having a state, (ii) F = (fi, fi, . . ., fn), with fi denoting a function associated with node ui E V and (iii) A is a permutation of (or total order on) the nodes in V, A configuration of an SDS is an n-vector ( b l, bz, . . ., bn), where bi is the value of the state of node vi. A single SDS transition from one configuration to another is obtained by updating the states of the nodes by evaluating the function associated with each of them in the order given by n. Here, we address the complexity of two basic problems and their generalizations for SDSs. Given an SDS S and a configuration C, the PREDECESSOR EXISTENCE (or PRE) problem is to determine whether there is a configuration C' such that S has a transition...

Research paper thumbnail of Active client primary-backup protocols

Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing - PODC '95, 1995

Research paper thumbnail of Analysis Problems for Sequential Dynamical Systems and Communicating State Machines

Lecture Notes in Computer Science, 2001

Abstract. Informally, a sequential dynamical system (SDS) consists of an undirected graph where e... more Abstract. Informally, a sequential dynamical system (SDS) consists of an undirected graph where each node v is associated with a state sv and a transition function fv. Given the state value sv and those of the neigh-bors of v, the function fv computes the next value of sv. The node ...

Research paper thumbnail of The complexity of testing predicate locks

Proceedings of the 1979 ACM SIGMOD international conference on Management of data - SIGMOD '79, 1979

Page 1. THE COMPLEXITY OF TESTING PREDICATE LOCKS Harry B. Hunt* ? : .! Department of Electrical ... more Page 1. THE COMPLEXITY OF TESTING PREDICATE LOCKS Harry B. Hunt* ? : .! Department of Electrical Engineering a&d Computer Science Columbia University New York, New York 10027 Daniel J. Posenkrantz** Computer ...

Research paper thumbnail of Theory of Periodically Specified Problems: Complexity and Approximabil ity

We study the complexity and the efficient approx- imability of graph and satisfiability problems ... more We study the complexity and the efficient approx- imability of graph and satisfiability problems when specified using various kinds of periodic specifica- tions studied in (Or82a, HT95, Wa93, HW94, Wa93, MH+94). We obtain two general results. First, we characterize the complexities of several basic gener- alized CNF satisfiability problems SAT(S) (Sc78), when instances are specified using various kinds of 1-

Research paper thumbnail of Structure-Based Resilience Metrics for Service-Oriented Networks

Lecture Notes in Computer Science, 2005

Many governmental agencies and businesses organizations use networked systems to provide a number... more Many governmental agencies and businesses organizations use networked systems to provide a number of services. Such a service-oriented network can be implemented as an overlay on top of the physical network. It is well recognized that the performance of many of the networked computer systems is severely degraded under node and edge failures. The focus of our work is on the resilience of service-oriented networks. We develop a graph theoretic model for service-oriented networks. Using this model, we propose metrics that quantify the resilience of such networks under node and edge failures. These metrics are based on the topological structure of the network and the manner in which services are distributed over the network. Based on this framework, we address two types of problems. The first type involves the analysis of a given network to determine its resilience parameters. The second type involves the design of networks with a given degree of resilience. We present efficient algorithms for both types of problems. Our approach for solving analysis problems relies on known algorithms for computing minimum cuts in graphs. Our algorithms for the design problem are based on a careful analysis of the decomposition of the given graph into appropriate types of connected components.

Research paper thumbnail of Processing Conjunctive Predicates and Queries

Very Large Data Bases, 1980

Google, Inc. (search), Subscribe (Full Service), Register (Limited Service, Free), Login. Search:... more Google, Inc. (search), Subscribe (Full Service), Register (Limited Service, Free), Login. Search: The ACM Digital Library The Guide. ...

Research paper thumbnail of Modeling and analyzing social network dynamics using stochastic discrete graphical dynamical systems

Theoretical Computer Science, 2011

... Moreover, the hardness results hold even when the underlying graph is a simple path. By a min... more ... Moreover, the hardness results hold even when the underlying graph is a simple path. By a minor modi cation to this proof, the hardness result can also be shown to hold for SSDSs (where nodes update their states sequentially). ...

Research paper thumbnail of Compact location problems

Lecture Notes in Computer Science, 1993

We consider the problem of placing a speci ed number (p) of facilities on the nodes of a network ... more We consider the problem of placing a speci ed number (p) of facilities on the nodes of a network so as to minimize some measure of the distances between facilities. This type of problem models a number of problems arising in facility location, statistical clustering, pattern recognition, and processor allocation problems in multiprocessor systems. We consider the problem under three di erent objectives, namely minimizing the diameter, minimizing the average distance, and minimizing the variance. We observe that in general, the problem is NP-hard under any of the objectives. Further, even obtaining a constant factor approximation for any of the objectives is NP-hard.

Research paper thumbnail of Parallel Approximation Schemes for a Class of Planar and Near Planar Combinatorial Optimization Problems

Information and Computation/information and Control, 2002

Define a (δ, g)-almost planar graph to be a graph G(V, E) consisting of vertex set V and a genus ... more Define a (δ, g)-almost planar graph to be a graph G(V, E) consisting of vertex set V and a genus g layout with at most δ·|V| crossover nodes. We study a class of combinatorial optimization problems formulated as follows. Let X={x1, x2,…xn} be a set of variables each of which has a finite domain D={0, 1,…,poly(n)}. Also, let S be

Research paper thumbnail of Deferred updates and data placement in distributed databases

Proceedings of the Twelfth International Conference on Data Engineering, 1996

Commercial distributed database systems generally support an optional protocol that provides loos... more Commercial distributed database systems generally support an optional protocol that provides loose consistency of replicas, allowing replicas to be inconsistent for some time. In such a protocol, each replicated data item is assigned a primary copy site. Typically, a transaction updates only the primary copies of data items, with updates to other copies deferred until after the transaction commits. After a transaction commits, its updates to primary copies are sent transactionally to the other sites containing secondary copies. We investigate the transaction model underlying the above protocol. We show that global serializability in such a system is a property of the placement of primary and secondary copies of replicated data items. We present a polynomial time algorithm to assign primary sites to data items so that the resulting topology ensures serializability.

Research paper thumbnail of Discovering Dynamic Developer Relationships from Software Version Histories by Time Series Segmentation

2007 IEEE International Conference on Software Maintenance, 2007

Time series analysis is a promising approach to discover temporal patterns from time stamped, num... more Time series analysis is a promising approach to discover temporal patterns from time stamped, numeric data. A novel approach to apply time series analysis to discern temporal information from software version repositories is proposed. Version logs containing numeric as well as nonnumeric data are represented as an item-set time series. A dynamic programming based algorithm to optimally segment an item-set time series is presented. The algorithm automatically produces a compacted item-set time series that can be analyzed to discern temporal patterns. The effectiveness of the approach is illustrated by applying to the Mozilla data set to study the change frequency and developer activity profiles. The experimental results show that the segmentation algorithm produces segments that capture meaningful information and is superior to the information content obtaining by arbitrarily segmenting time period into regular time intervals.

Research paper thumbnail of On the complexity of relational problems for finite state processes

We study the complexity of the following two relational problems: Let be a binary relation on nit... more We study the complexity of the following two relational problems: Let be a binary relation on nite state processes; and let p0 be a xed nite state process. P1: Determine for processes p and q, if p q. P2: Determine for process p, if p p0. We study the complexities of these problems, when processes are represented by sequential transition systems and by parallel composition of transition systems.

Research paper thumbnail of HORNSAT, model checking, verification and games

We develop a methodology based upon HORNSAT for model checking and for checking behavioral relati... more We develop a methodology based upon HORNSAT for model checking and for checking behavioral relations between nite state processes. This methodology has a number of advantages, previously only obtained in di erent solutions of some of these problems. For example, our methodology can be used to generate diagnostic information CC92] e ciently. It can be used to do model checking e ciently, for various fragments of modal mu-calculus. It is naturally local SW91, Lar92]; and it can be made to run both on the y VW86, CVWY92, FM91, BCG95] and incrementally SS94].

Research paper thumbnail of Facility dispersion problems: Heuristics and special cases

Lecture Notes in Computer Science, 1991

ABSTRACT Facility dispersion problem deals with the location of facilities on a network so as to ... more ABSTRACT Facility dispersion problem deals with the location of facilities on a network so as to maximize some function of the distances between facilities. We consider the problem under two different optimality criteria, namely maximizing the minimum distance (MAX-MIN) between any pair of facilities and maximizing the average distance (MAX-AVG) between any pair of facilities. Under either criterion, the problem is known to be NP-hard, even when the distances satisfy the triangle inequality. We consider the question of obtaining near-optimal solutions. For the MAX-MIN criterion, we show that if the distances do not satisfy the triangle inequality, there is no polynomial time relative approximation algorithm unless P=NP. When the distances do satisfy the triangle inequality, we present an efficient heuristic which provides a performance guarantee of 2, thus improving the performance guarantee of 3 proven in [Wh91]. We also prove that obtaining a performance guarantee of less than 2 is NP-hard. For the MAX-AVG criterion, we present a heuristic which provides a performance guarantee of 4, provided that the distances satisfy the triangle inequality. For the 1-dimensional dispersion problem, we provide polynomial time algorithms for obtaining optimal solutions under both MAX-MIN and MAX-AVG criteria. Using the latter algorithm, we obtain a heuristic which provides a performance guarantee of 4( Ö2 - 1\sqrt 2 - 1 ) 1.657 for the 2-dimensional dispersion problem under the MAX-AVG criterion.

Research paper thumbnail of Facility Dispersion Problems: Heuristics and Special Cases (Extended Abstract)

Workshop on Algorithms and Data Structures, 1991

ABSTRACT Facility dispersion problem deals with the location of facilities on a network so as to ... more ABSTRACT Facility dispersion problem deals with the location of facilities on a network so as to maximize some function of the distances between facilities. We consider the problem under two different optimality criteria, namely maximizing the minimum distance (MAX-MIN) between any pair of facilities and maximizing the average distance (MAX-AVG) between any pair of facilities. Under either criterion, the problem is known to be NP-hard, even when the distances satisfy the triangle inequality. We consider the question of obtaining near-optimal solutions. For the MAX-MIN criterion, we show that if the distances do not satisfy the triangle inequality, there is no polynomial time relative approximation algorithm unless P=NP. When the distances do satisfy the triangle inequality, we present an efficient heuristic which provides a performance guarantee of 2, thus improving the performance guarantee of 3 proven in [Wh91]. We also prove that obtaining a performance guarantee of less than 2 is NP-hard. For the MAX-AVG criterion, we present a heuristic which provides a performance guarantee of 4, provided that the distances satisfy the triangle inequality. For the 1-dimensional dispersion problem, we provide polynomial time algorithms for obtaining optimal solutions under both MAX-MIN and MAX-AVG criteria. Using the latter algorithm, we obtain a heuristic which provides a performance guarantee of 4( Ö2 - 1\sqrt 2 - 1 ) 1.657 for the 2-dimensional dispersion problem under the MAX-AVG criterion.

Research paper thumbnail of On Materializations of Array-Valued Temporaries

Lecture Notes in Computer Science, 2001

We present results demonstrating the usefulness of monolithic program analysis and optimization p... more We present results demonstrating the usefulness of monolithic program analysis and optimization prior to scalarization. In particular, models are developed for studying nonmaterialization in basic blocks consisting ofa sequence of assignment statements involving array- valued variables. We use these models to analyze the problem ofmi nimizing the number ofmat erializations in a basic block, and to develop an efficient algorithm for minimizing the number of materializations in certain cases.

Research paper thumbnail of Distributed database concurrency controls using before-values

Proceedings of the 1981 ACM SIGMOD international conference on Management of data - SIGMOD '81, 1981

Associated with the write of a database entity is both the &a... more Associated with the write of a database entity is both the "before" or old value, and the "after" or new value. Concurrency can be increased by allowing other transactions to read the before values of a given transaction. The ramifications of allowing this, particularly on a distributed system in which limited communications is desirable, are investigated. A careful distinction is

Research paper thumbnail of Sequential dynamical systems with threshold functions

A sequential dynamical system (SDS) (see [BH+01] and the references therein) consists of an undir... more A sequential dynamical system (SDS) (see [BH+01] and the references therein) consists of an undirected graph G(V,E) where each node V is associated with a Boolean state (s{sub }) and a symmetric Boolean function f{sub } (called the local transition function at ). The inputs to f{sub } are s{sub } and the states of all the nodes adjacent to . In each step of the SDS, the nodes update their state values using their local transition functions in the order specified by a given permutation of the nodes. A configuration of the SDS is an n-tuple (b, b...,b{sub n}) where n = |V| and b{sub i} {l_brace}0,1{r_brace} is the state value of node {sub i}. The system starts in a specified initial configuration and each step of the SDS produces a (possibly new) configuration.

Research paper thumbnail of Segmentation of Time Series Data

Segmentation of Time Series Data (9781605660103): Parvathi Chundi, Daniel J. Rosenkrantz: Book Ch... more Segmentation of Time Series Data (9781605660103): Parvathi Chundi, Daniel J. Rosenkrantz: Book Chapters.

Research paper thumbnail of Predecessor and Permutation Existence Problems for Sequential Dynamical Systems

A class of finite discrete dynamical systems, called Sequential Dynamical Systems (SDSs), was int... more A class of finite discrete dynamical systems, called Sequential Dynamical Systems (SDSs), was introduced in BMR99, BR991 as a formal model for analyzing simulation systems. An SDS S is a triple (G, F,n ),w here (i) G(V,E ) is an undirected graph with n nodes with each node having a state, (ii) F = (fi, fi, . . ., fn), with fi denoting a function associated with node ui E V and (iii) A is a permutation of (or total order on) the nodes in V, A configuration of an SDS is an n-vector ( b l, bz, . . ., bn), where bi is the value of the state of node vi. A single SDS transition from one configuration to another is obtained by updating the states of the nodes by evaluating the function associated with each of them in the order given by n. Here, we address the complexity of two basic problems and their generalizations for SDSs. Given an SDS S and a configuration C, the PREDECESSOR EXISTENCE (or PRE) problem is to determine whether there is a configuration C' such that S has a transition...

Research paper thumbnail of Active client primary-backup protocols

Proceedings of the fourteenth annual ACM symposium on Principles of distributed computing - PODC '95, 1995

Research paper thumbnail of Analysis Problems for Sequential Dynamical Systems and Communicating State Machines

Lecture Notes in Computer Science, 2001

Abstract. Informally, a sequential dynamical system (SDS) consists of an undirected graph where e... more Abstract. Informally, a sequential dynamical system (SDS) consists of an undirected graph where each node v is associated with a state sv and a transition function fv. Given the state value sv and those of the neigh-bors of v, the function fv computes the next value of sv. The node ...

Research paper thumbnail of The complexity of testing predicate locks

Proceedings of the 1979 ACM SIGMOD international conference on Management of data - SIGMOD '79, 1979

Page 1. THE COMPLEXITY OF TESTING PREDICATE LOCKS Harry B. Hunt* ? : .! Department of Electrical ... more Page 1. THE COMPLEXITY OF TESTING PREDICATE LOCKS Harry B. Hunt* ? : .! Department of Electrical Engineering a&d Computer Science Columbia University New York, New York 10027 Daniel J. Posenkrantz** Computer ...

Research paper thumbnail of Theory of Periodically Specified Problems: Complexity and Approximabil ity

We study the complexity and the efficient approx- imability of graph and satisfiability problems ... more We study the complexity and the efficient approx- imability of graph and satisfiability problems when specified using various kinds of periodic specifica- tions studied in (Or82a, HT95, Wa93, HW94, Wa93, MH+94). We obtain two general results. First, we characterize the complexities of several basic gener- alized CNF satisfiability problems SAT(S) (Sc78), when instances are specified using various kinds of 1-

Research paper thumbnail of Structure-Based Resilience Metrics for Service-Oriented Networks

Lecture Notes in Computer Science, 2005

Many governmental agencies and businesses organizations use networked systems to provide a number... more Many governmental agencies and businesses organizations use networked systems to provide a number of services. Such a service-oriented network can be implemented as an overlay on top of the physical network. It is well recognized that the performance of many of the networked computer systems is severely degraded under node and edge failures. The focus of our work is on the resilience of service-oriented networks. We develop a graph theoretic model for service-oriented networks. Using this model, we propose metrics that quantify the resilience of such networks under node and edge failures. These metrics are based on the topological structure of the network and the manner in which services are distributed over the network. Based on this framework, we address two types of problems. The first type involves the analysis of a given network to determine its resilience parameters. The second type involves the design of networks with a given degree of resilience. We present efficient algorithms for both types of problems. Our approach for solving analysis problems relies on known algorithms for computing minimum cuts in graphs. Our algorithms for the design problem are based on a careful analysis of the decomposition of the given graph into appropriate types of connected components.

Research paper thumbnail of Processing Conjunctive Predicates and Queries

Very Large Data Bases, 1980

Google, Inc. (search), Subscribe (Full Service), Register (Limited Service, Free), Login. Search:... more Google, Inc. (search), Subscribe (Full Service), Register (Limited Service, Free), Login. Search: The ACM Digital Library The Guide. ...

Research paper thumbnail of Modeling and analyzing social network dynamics using stochastic discrete graphical dynamical systems

Theoretical Computer Science, 2011

... Moreover, the hardness results hold even when the underlying graph is a simple path. By a min... more ... Moreover, the hardness results hold even when the underlying graph is a simple path. By a minor modi cation to this proof, the hardness result can also be shown to hold for SSDSs (where nodes update their states sequentially). ...

Research paper thumbnail of Compact location problems

Lecture Notes in Computer Science, 1993

We consider the problem of placing a speci ed number (p) of facilities on the nodes of a network ... more We consider the problem of placing a speci ed number (p) of facilities on the nodes of a network so as to minimize some measure of the distances between facilities. This type of problem models a number of problems arising in facility location, statistical clustering, pattern recognition, and processor allocation problems in multiprocessor systems. We consider the problem under three di erent objectives, namely minimizing the diameter, minimizing the average distance, and minimizing the variance. We observe that in general, the problem is NP-hard under any of the objectives. Further, even obtaining a constant factor approximation for any of the objectives is NP-hard.

Research paper thumbnail of Parallel Approximation Schemes for a Class of Planar and Near Planar Combinatorial Optimization Problems

Information and Computation/information and Control, 2002

Define a (δ, g)-almost planar graph to be a graph G(V, E) consisting of vertex set V and a genus ... more Define a (δ, g)-almost planar graph to be a graph G(V, E) consisting of vertex set V and a genus g layout with at most δ·|V| crossover nodes. We study a class of combinatorial optimization problems formulated as follows. Let X={x1, x2,…xn} be a set of variables each of which has a finite domain D={0, 1,…,poly(n)}. Also, let S be

Research paper thumbnail of Deferred updates and data placement in distributed databases

Proceedings of the Twelfth International Conference on Data Engineering, 1996

Commercial distributed database systems generally support an optional protocol that provides loos... more Commercial distributed database systems generally support an optional protocol that provides loose consistency of replicas, allowing replicas to be inconsistent for some time. In such a protocol, each replicated data item is assigned a primary copy site. Typically, a transaction updates only the primary copies of data items, with updates to other copies deferred until after the transaction commits. After a transaction commits, its updates to primary copies are sent transactionally to the other sites containing secondary copies. We investigate the transaction model underlying the above protocol. We show that global serializability in such a system is a property of the placement of primary and secondary copies of replicated data items. We present a polynomial time algorithm to assign primary sites to data items so that the resulting topology ensures serializability.

Research paper thumbnail of Discovering Dynamic Developer Relationships from Software Version Histories by Time Series Segmentation

2007 IEEE International Conference on Software Maintenance, 2007

Time series analysis is a promising approach to discover temporal patterns from time stamped, num... more Time series analysis is a promising approach to discover temporal patterns from time stamped, numeric data. A novel approach to apply time series analysis to discern temporal information from software version repositories is proposed. Version logs containing numeric as well as nonnumeric data are represented as an item-set time series. A dynamic programming based algorithm to optimally segment an item-set time series is presented. The algorithm automatically produces a compacted item-set time series that can be analyzed to discern temporal patterns. The effectiveness of the approach is illustrated by applying to the Mozilla data set to study the change frequency and developer activity profiles. The experimental results show that the segmentation algorithm produces segments that capture meaningful information and is superior to the information content obtaining by arbitrarily segmenting time period into regular time intervals.

Research paper thumbnail of On the complexity of relational problems for finite state processes

We study the complexity of the following two relational problems: Let be a binary relation on nit... more We study the complexity of the following two relational problems: Let be a binary relation on nite state processes; and let p0 be a xed nite state process. P1: Determine for processes p and q, if p q. P2: Determine for process p, if p p0. We study the complexities of these problems, when processes are represented by sequential transition systems and by parallel composition of transition systems.

Research paper thumbnail of HORNSAT, model checking, verification and games

We develop a methodology based upon HORNSAT for model checking and for checking behavioral relati... more We develop a methodology based upon HORNSAT for model checking and for checking behavioral relations between nite state processes. This methodology has a number of advantages, previously only obtained in di erent solutions of some of these problems. For example, our methodology can be used to generate diagnostic information CC92] e ciently. It can be used to do model checking e ciently, for various fragments of modal mu-calculus. It is naturally local SW91, Lar92]; and it can be made to run both on the y VW86, CVWY92, FM91, BCG95] and incrementally SS94].

Research paper thumbnail of Facility dispersion problems: Heuristics and special cases

Lecture Notes in Computer Science, 1991

ABSTRACT Facility dispersion problem deals with the location of facilities on a network so as to ... more ABSTRACT Facility dispersion problem deals with the location of facilities on a network so as to maximize some function of the distances between facilities. We consider the problem under two different optimality criteria, namely maximizing the minimum distance (MAX-MIN) between any pair of facilities and maximizing the average distance (MAX-AVG) between any pair of facilities. Under either criterion, the problem is known to be NP-hard, even when the distances satisfy the triangle inequality. We consider the question of obtaining near-optimal solutions. For the MAX-MIN criterion, we show that if the distances do not satisfy the triangle inequality, there is no polynomial time relative approximation algorithm unless P=NP. When the distances do satisfy the triangle inequality, we present an efficient heuristic which provides a performance guarantee of 2, thus improving the performance guarantee of 3 proven in [Wh91]. We also prove that obtaining a performance guarantee of less than 2 is NP-hard. For the MAX-AVG criterion, we present a heuristic which provides a performance guarantee of 4, provided that the distances satisfy the triangle inequality. For the 1-dimensional dispersion problem, we provide polynomial time algorithms for obtaining optimal solutions under both MAX-MIN and MAX-AVG criteria. Using the latter algorithm, we obtain a heuristic which provides a performance guarantee of 4( Ö2 - 1\sqrt 2 - 1 ) 1.657 for the 2-dimensional dispersion problem under the MAX-AVG criterion.