Eli Gafni - Profile on Academia.edu (original) (raw)
Papers by Eli Gafni
SIAM Journal on Discrete Mathematics, 2014
In the musical chairs game MC(n, m), a team of n players plays against an adversarial scheduler. ... more In the musical chairs game MC(n, m), a team of n players plays against an adversarial scheduler. The scheduler wins if the game proceeds indefinitely, while termination after a finite number of rounds is declared a win of the team. At each round of the game each player occupies one of the m available chairs. Termination (and a win of the team) is declared as soon as each player occupies a unique chair. Two players that simultaneously occupy the same chair are said to be in conflict. In other words, termination (and a win for the team) is reached as soon as there are no conflicts. The only means of communication throughout the game is this: At every round of the game, the scheduler selects an arbitrary nonempty set of players who are currently in conflict, and notifies each of them separately that it must move. A player who is thus notified changes its chair according to its deterministic program. As we show, for m ≥ 2n -1 chairs the team has a winning strategy. Moreover, using topological arguments we show that this bound is tight. For m ≤ 2n -2 the scheduler has a strategy that is guaranteed to make the game continue indefinitely and thus win. We also have some results on additional interesting questions. For example, if m ≥ 2n -1 (so that the team can win), how quickly can they achieve victory?
Theoretical Computer Science, 1987
A multi-channel broadcast network is a distributed computation model in which p independent proce... more A multi-channel broadcast network is a distributed computation model in which p independent processors communicate over a set of p shared broadcast channels. Computation proceeds in synchronous cycles, during each of which the processors first write and read the channels, then perform local computations. Performance is measured in terms of the number of cycles used in the computation, where each bit to be transmitted is assumed to require a separate cycle. In this paper we investigate the problem of sorting p bit strings of uniform length m, each string initially located at a different processor in the broadcast network. We develop an efficient sorting method that first reduces the length of the strings without affecting their relative order, then proceeds using only the shorter strings. A sequence of three successively improved algorithms based on this approach is presented, the best of which runs in O(m +p log p) cycles. By showing a lower bound of n(m) cycles, we prove th&c: the algorithm is optimal for sufficiently large m. Our results improve by a factor of logp the solution of the multiple identification problem presented by Landau, Yung and Galil (1985).
Lecture Notes in Computer Science, Sep 22, 2008
We propose and solve a synchronization problem called the mailbox problem, motivated by a particu... more We propose and solve a synchronization problem called the mailbox problem, motivated by a particular type of interaction between a processor and an external device or between two threads. In this problem, a postman delivers letters to the mailbox of a home owner and uses a flag to signal a non-empty mailbox. The owner must remove all letters delivered to the mailbox and should not walk to the mailbox if it is empty. We present algorithms and an impossibility result for this problem.
This paper addresses the problem of distributively electing a leader in both synchronous and asyn... more This paper addresses the problem of distributively electing a leader in both synchronous and asynchronous complete networks. In the synchronous case, we prove a lower bound of ft(n'logn) on the message complexity. We also prove that any message-optimal synchronous algorithm requires ~(log n) time. In proving these bounds we do not restrict the type of operations performed by nodes. The bounds thus apply to general algorithms and not just to comparison based algorithms. A simple algorithm which achieves these bounds is presented. In the asynchronous case, we present a sequence of three simple and efficient algorithms, each of which is an improvement on the previous. The third algorithm has time complexity O(n) and message complexity 2.n.logn+O(n), thus improving the time complexity of the previous best algorithm [Kor84] by a factor of logn. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission.
SIAM Journal on Computing, 1998
We show that no algorithm exists for deciding whether a nite task for three or more processors is... more We show that no algorithm exists for deciding whether a nite task for three or more processors is wait-free solvable in the asynchronous read-write shared-memory model. This impossibility result implies that there is no constructive (recursive) characterization of wait-free solvable tasks. It also applies to other shared-memory models of distributed computing, such as the comparison-based model.
Lecture Notes in Computer Science, 2013
We consider synchronous dynamic networks which like radio networks may have asymmetric communicat... more We consider synchronous dynamic networks which like radio networks may have asymmetric communication links, and are affected by communication rather than processor failures. In this paper we investigate the minimal message survivability in a per round basis that allows for the minimal global cooperation, i.e., allows to solve any task that is wait-free read-write solvable. The paper completely characterizes this survivability requirement. Message survivability is formalized by considering adversaries that have a limited power to remove messages in a round. Removal of a message on a link in one direction does not necessarily imply the removal of the message on that link in the other direction. Surprisingly there exist a single strongest adversary which solves any wait-free read/write task. Any different adversary that solves any wait-free read/write task is weaker, and any stronger adversary will not solve any wait-free read/write task. ABD [6] who considered processor failure, arrived at an adversary that is n/2 resilient, consequently can solve tasks, such as n/2-set-consensus, which are not read/write wait-free solvable. With message adversaries, we arrive at an adversary which has exactly the read-write wait-free power. Furthermore, this adversary allows for a considerably simpler (simplest that we know of) proof that the protocol complex of any read/write wait-free task is a subdivided simplex, finally making this proof accessible for students with no algebraic-topology prerequisites, and alternatively dispensing with the assumption that the Immediate Snapshot complex is a subdivided simplex.
Lecture Notes in Computer Science, 2000
We present an algorithm, called Disk Paxos, for implementing a reliable distributed system with a... more We present an algorithm, called Disk Paxos, for implementing a reliable distributed system with a network of processors and disks. Like the original Paxos algorithm, Disk Paxos maintains consistency in the presence of arbitrary non-Byzantine faults. Progress can be guaranteed as long as a majority of the disks are available, even if all processors but one have failed. Phase 1 Choose a value v . 1 There is also an extra phase that a processor executes when recovering from a failure. 2 If processor p fails, it can restart with a new value of input[p].
Springer eBooks, 1992
This paper presents an economical, randomized, wait-free construction of an n-process test-and-se... more This paper presents an economical, randomized, wait-free construction of an n-process test-and-set bit from read write registers. The test-and-set shared object has two atomic operations, test&set, which atomically reads the bit and sets its value to 1, and the reset operation that resets the bit to 0. We identify two new complexity measures by which to evaluate waitfree algorithms: (a) The amount of randomness used, and (b) 'Parallel-Time'--the maximum sequential depth of an execution (i.e. longest chain of operations that must precede each other). The previously best known algorithm for n-process test-and-set [Hergl] takes an expected S2(n 2) parallel time, and C2(n 4) sequential time per operation, and ~(n 2 log n) space per processor. In contrast, our direct implementation improves this on all counts by using O(log n) coin flips, O(logn) parallel time, O(n) sequential time, per operation, and O(n) space per processor. Thus the question on the difference in the expected complexity of randomized constructions of concurrent objects from read/write registers is raised.
Local fail-safe network reset procedure
Springer eBooks, 1988
ABSTRACT A simple, general and optimal procedure to adapt algorithms designed for fixed topology ... more ABSTRACT A simple, general and optimal procedure to adapt algorithms designed for fixed topology networks to run on a network with dynamically changing topology is presented. The communication and time complexities of the procedure, per topological change, are independent of the number of topological changes and are linearly bounded by the size of the subnetwork over which the algorithm is running.
Common2, the family of objects that implement and are wait-free implementable from 2 consensus ob... more Common2, the family of objects that implement and are wait-free implementable from 2 consensus objects, is extended inhere in two ways: First, the stack object is added to the family -an object that was conjectured not to be in the family. Second, Common2 is investigated in the unbounded concurrency model, whereas until now it was considered only in an n-process model. We show that fetch-and-add, test-and-set, and stack are in Common2 even with respect to this stronger notion of wait-free implementation. This necessitated the wait-free implementation of immediate snapshots in the unbounded concurrency model, which was previously not known to be possible. In addition to extending Common2, the introduction of unbounded-concurrency may help in resolving the Common2 membership problem: If, as conjectured, queue is not implementable for a-priori known concurrency n, then it is definitely not implementable for unbounded concurrency. Proving the latter should be easier than proving the former. In addition we conjecture that the swap object, that has an nprocess implementation, does not have an unbounded concurrency implementation.
A bounded first-in, first-enabled solution to th el-exclusion problem
Acm Transactions on Programming Languages and Systems, 1994
An O(n^2 m^1/2) Distributed Max-Flow Algorithm
Sorting and Selection in MultiChannel Broadcast Networks
International Conference on Parallel Processing, 1985
Upper and lower bounds for routing schemes in dynamic networks
30th Annual Symposium on Foundations of Computer Science, 1989
ABSTRACT
On using network attached disks as shared memory
Proceedings of the twenty-second annual symposium on Principles of distributed computing, 2003
Local fail-safe network reset procedure
Lecture Notes in Computer Science, 1988
ABSTRACT A simple, general and optimal procedure to adapt algorithms designed for fixed topology ... more ABSTRACT A simple, general and optimal procedure to adapt algorithms designed for fixed topology networks to run on a network with dynamically changing topology is presented. The communication and time complexities of the procedure, per topological change, are independent of the number of topological changes and are linearly bounded by the size of the subnetwork over which the algorithm is running.
3Processor Tasks Are Undecidable (Abstract)
Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing - PODC '16, 2016
Adaptive renaming can be viewed as a coordination task involving a set of asynchronous agents, ea... more Adaptive renaming can be viewed as a coordination task involving a set of asynchronous agents, each aiming at grabbing a single resource out of a set of resources totally ordered by their desirability. We consider a generalization of adaptive renaming to take into account scenarios in which resources are not independent. We model constraints between resources as an undirected graph: nodes represent the ressources, and an edge between two ressources indicates that these two ressources cannot be used simultaneously. In such a setting, the sets of resources that processes may use simultaneously form independent sets. In this note, we focus on this task in a model where such independent sets are computed by wait-free processes.
Distributed Computing, Nov 3, 2009
This paper introduces and investigates the k-simultaneous consensus problem: each process partici... more This paper introduces and investigates the k-simultaneous consensus problem: each process participates at the same time in k independent consensus instances until it decides in any one of them. Two results are presented. The first shows that the k-simultaneous consensus problem and the k-set agreement problem are wait-free equivalent in read/write shared memory systems. The second shows that the multivalued version and the binary version of the k-simultaneous consensus problem are wait-free equivalent. These equivalences are independent of the number of processes. An immediate consequence of these results is that the k-set agreement problem and the k-simultaneous binary consensus problem are equivalent. This not only provides a new characterization of the k-set agreement problem but also provides a meaning to the notion of k-set binary agreement.
SIAM Journal on Discrete Mathematics, 2014
In the musical chairs game MC(n, m), a team of n players plays against an adversarial scheduler. ... more In the musical chairs game MC(n, m), a team of n players plays against an adversarial scheduler. The scheduler wins if the game proceeds indefinitely, while termination after a finite number of rounds is declared a win of the team. At each round of the game each player occupies one of the m available chairs. Termination (and a win of the team) is declared as soon as each player occupies a unique chair. Two players that simultaneously occupy the same chair are said to be in conflict. In other words, termination (and a win for the team) is reached as soon as there are no conflicts. The only means of communication throughout the game is this: At every round of the game, the scheduler selects an arbitrary nonempty set of players who are currently in conflict, and notifies each of them separately that it must move. A player who is thus notified changes its chair according to its deterministic program. As we show, for m ≥ 2n -1 chairs the team has a winning strategy. Moreover, using topological arguments we show that this bound is tight. For m ≤ 2n -2 the scheduler has a strategy that is guaranteed to make the game continue indefinitely and thus win. We also have some results on additional interesting questions. For example, if m ≥ 2n -1 (so that the team can win), how quickly can they achieve victory?
Theoretical Computer Science, 1987
A multi-channel broadcast network is a distributed computation model in which p independent proce... more A multi-channel broadcast network is a distributed computation model in which p independent processors communicate over a set of p shared broadcast channels. Computation proceeds in synchronous cycles, during each of which the processors first write and read the channels, then perform local computations. Performance is measured in terms of the number of cycles used in the computation, where each bit to be transmitted is assumed to require a separate cycle. In this paper we investigate the problem of sorting p bit strings of uniform length m, each string initially located at a different processor in the broadcast network. We develop an efficient sorting method that first reduces the length of the strings without affecting their relative order, then proceeds using only the shorter strings. A sequence of three successively improved algorithms based on this approach is presented, the best of which runs in O(m +p log p) cycles. By showing a lower bound of n(m) cycles, we prove th&c: the algorithm is optimal for sufficiently large m. Our results improve by a factor of logp the solution of the multiple identification problem presented by Landau, Yung and Galil (1985).
Lecture Notes in Computer Science, Sep 22, 2008
We propose and solve a synchronization problem called the mailbox problem, motivated by a particu... more We propose and solve a synchronization problem called the mailbox problem, motivated by a particular type of interaction between a processor and an external device or between two threads. In this problem, a postman delivers letters to the mailbox of a home owner and uses a flag to signal a non-empty mailbox. The owner must remove all letters delivered to the mailbox and should not walk to the mailbox if it is empty. We present algorithms and an impossibility result for this problem.
This paper addresses the problem of distributively electing a leader in both synchronous and asyn... more This paper addresses the problem of distributively electing a leader in both synchronous and asynchronous complete networks. In the synchronous case, we prove a lower bound of ft(n'logn) on the message complexity. We also prove that any message-optimal synchronous algorithm requires ~(log n) time. In proving these bounds we do not restrict the type of operations performed by nodes. The bounds thus apply to general algorithms and not just to comparison based algorithms. A simple algorithm which achieves these bounds is presented. In the asynchronous case, we present a sequence of three simple and efficient algorithms, each of which is an improvement on the previous. The third algorithm has time complexity O(n) and message complexity 2.n.logn+O(n), thus improving the time complexity of the previous best algorithm [Kor84] by a factor of logn. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission.
SIAM Journal on Computing, 1998
We show that no algorithm exists for deciding whether a nite task for three or more processors is... more We show that no algorithm exists for deciding whether a nite task for three or more processors is wait-free solvable in the asynchronous read-write shared-memory model. This impossibility result implies that there is no constructive (recursive) characterization of wait-free solvable tasks. It also applies to other shared-memory models of distributed computing, such as the comparison-based model.
Lecture Notes in Computer Science, 2013
We consider synchronous dynamic networks which like radio networks may have asymmetric communicat... more We consider synchronous dynamic networks which like radio networks may have asymmetric communication links, and are affected by communication rather than processor failures. In this paper we investigate the minimal message survivability in a per round basis that allows for the minimal global cooperation, i.e., allows to solve any task that is wait-free read-write solvable. The paper completely characterizes this survivability requirement. Message survivability is formalized by considering adversaries that have a limited power to remove messages in a round. Removal of a message on a link in one direction does not necessarily imply the removal of the message on that link in the other direction. Surprisingly there exist a single strongest adversary which solves any wait-free read/write task. Any different adversary that solves any wait-free read/write task is weaker, and any stronger adversary will not solve any wait-free read/write task. ABD [6] who considered processor failure, arrived at an adversary that is n/2 resilient, consequently can solve tasks, such as n/2-set-consensus, which are not read/write wait-free solvable. With message adversaries, we arrive at an adversary which has exactly the read-write wait-free power. Furthermore, this adversary allows for a considerably simpler (simplest that we know of) proof that the protocol complex of any read/write wait-free task is a subdivided simplex, finally making this proof accessible for students with no algebraic-topology prerequisites, and alternatively dispensing with the assumption that the Immediate Snapshot complex is a subdivided simplex.
Lecture Notes in Computer Science, 2000
We present an algorithm, called Disk Paxos, for implementing a reliable distributed system with a... more We present an algorithm, called Disk Paxos, for implementing a reliable distributed system with a network of processors and disks. Like the original Paxos algorithm, Disk Paxos maintains consistency in the presence of arbitrary non-Byzantine faults. Progress can be guaranteed as long as a majority of the disks are available, even if all processors but one have failed. Phase 1 Choose a value v . 1 There is also an extra phase that a processor executes when recovering from a failure. 2 If processor p fails, it can restart with a new value of input[p].
Springer eBooks, 1992
This paper presents an economical, randomized, wait-free construction of an n-process test-and-se... more This paper presents an economical, randomized, wait-free construction of an n-process test-and-set bit from read write registers. The test-and-set shared object has two atomic operations, test&set, which atomically reads the bit and sets its value to 1, and the reset operation that resets the bit to 0. We identify two new complexity measures by which to evaluate waitfree algorithms: (a) The amount of randomness used, and (b) 'Parallel-Time'--the maximum sequential depth of an execution (i.e. longest chain of operations that must precede each other). The previously best known algorithm for n-process test-and-set [Hergl] takes an expected S2(n 2) parallel time, and C2(n 4) sequential time per operation, and ~(n 2 log n) space per processor. In contrast, our direct implementation improves this on all counts by using O(log n) coin flips, O(logn) parallel time, O(n) sequential time, per operation, and O(n) space per processor. Thus the question on the difference in the expected complexity of randomized constructions of concurrent objects from read/write registers is raised.
Local fail-safe network reset procedure
Springer eBooks, 1988
ABSTRACT A simple, general and optimal procedure to adapt algorithms designed for fixed topology ... more ABSTRACT A simple, general and optimal procedure to adapt algorithms designed for fixed topology networks to run on a network with dynamically changing topology is presented. The communication and time complexities of the procedure, per topological change, are independent of the number of topological changes and are linearly bounded by the size of the subnetwork over which the algorithm is running.
Common2, the family of objects that implement and are wait-free implementable from 2 consensus ob... more Common2, the family of objects that implement and are wait-free implementable from 2 consensus objects, is extended inhere in two ways: First, the stack object is added to the family -an object that was conjectured not to be in the family. Second, Common2 is investigated in the unbounded concurrency model, whereas until now it was considered only in an n-process model. We show that fetch-and-add, test-and-set, and stack are in Common2 even with respect to this stronger notion of wait-free implementation. This necessitated the wait-free implementation of immediate snapshots in the unbounded concurrency model, which was previously not known to be possible. In addition to extending Common2, the introduction of unbounded-concurrency may help in resolving the Common2 membership problem: If, as conjectured, queue is not implementable for a-priori known concurrency n, then it is definitely not implementable for unbounded concurrency. Proving the latter should be easier than proving the former. In addition we conjecture that the swap object, that has an nprocess implementation, does not have an unbounded concurrency implementation.
A bounded first-in, first-enabled solution to th el-exclusion problem
Acm Transactions on Programming Languages and Systems, 1994
An O(n^2 m^1/2) Distributed Max-Flow Algorithm
Sorting and Selection in MultiChannel Broadcast Networks
International Conference on Parallel Processing, 1985
Upper and lower bounds for routing schemes in dynamic networks
30th Annual Symposium on Foundations of Computer Science, 1989
ABSTRACT
On using network attached disks as shared memory
Proceedings of the twenty-second annual symposium on Principles of distributed computing, 2003
Local fail-safe network reset procedure
Lecture Notes in Computer Science, 1988
ABSTRACT A simple, general and optimal procedure to adapt algorithms designed for fixed topology ... more ABSTRACT A simple, general and optimal procedure to adapt algorithms designed for fixed topology networks to run on a network with dynamically changing topology is presented. The communication and time complexities of the procedure, per topological change, are independent of the number of topological changes and are linearly bounded by the size of the subnetwork over which the algorithm is running.
3Processor Tasks Are Undecidable (Abstract)
Proceedings of the 2016 ACM Symposium on Principles of Distributed Computing - PODC '16, 2016
Adaptive renaming can be viewed as a coordination task involving a set of asynchronous agents, ea... more Adaptive renaming can be viewed as a coordination task involving a set of asynchronous agents, each aiming at grabbing a single resource out of a set of resources totally ordered by their desirability. We consider a generalization of adaptive renaming to take into account scenarios in which resources are not independent. We model constraints between resources as an undirected graph: nodes represent the ressources, and an edge between two ressources indicates that these two ressources cannot be used simultaneously. In such a setting, the sets of resources that processes may use simultaneously form independent sets. In this note, we focus on this task in a model where such independent sets are computed by wait-free processes.
Distributed Computing, Nov 3, 2009
This paper introduces and investigates the k-simultaneous consensus problem: each process partici... more This paper introduces and investigates the k-simultaneous consensus problem: each process participates at the same time in k independent consensus instances until it decides in any one of them. Two results are presented. The first shows that the k-simultaneous consensus problem and the k-set agreement problem are wait-free equivalent in read/write shared memory systems. The second shows that the multivalued version and the binary version of the k-simultaneous consensus problem are wait-free equivalent. These equivalences are independent of the number of processes. An immediate consequence of these results is that the k-set agreement problem and the k-simultaneous binary consensus problem are equivalent. This not only provides a new characterization of the k-set agreement problem but also provides a meaning to the notion of k-set binary agreement.