Shlomo Moran

Technion – Israel Institute of Technology | technion · Faculty of Computer Science

We study several variants of a combinatorial game which is based on Cantor's diagonal argument. The game is between two players called Kronecker and Cantor. The names of the players are motivated by the known fact that Leopold Kronecker did not appreciate Georg Cantor's arguments about the infinite, and even referred to him as a "scientific charlat...

The question whether one way functions (i.e., functions that are easy to compute but hard to invert) exist is arguably one of the central problems in complexity theory, both from theoretical and practical aspects. While proving that such functions exist could be hard, there were quite a few attempts to provide functions which are one way “in practi...

In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The user may run one algorithm at a time for the specified cost, or give up and pay the penalty. The probability of...

“Real Normed Algebras Revisited,” the last paper of the late Gadi Moran, attempts to reconstruct the discovery of the complex numbers, the quaternions, and the octonions, as well as proofs of their properties, using only what was known to 19th-century mathematicians. In his research, Gadi had discovered simple and elegant proofs of the above-mentio...

In the stabilizing consensus problem each agent of a networked system has an input value and is repeatedly writing an output value; it is required that eventually all the output values stabilize to the same value which, moreover, must be one of the input values. We study this problem for a synchronous model with identical and anonymous agents that...

In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The user may run one algorithm at a time for the specified cost, or give up and pay the penalty. The probability of...

"Real Normed Algebras Revisited", the last paper of the late Gadi Moran, attempts to reconstruct the discovery of the complex numbers, the quaternions and the octonions, as well as proofs of their properties, using only what was known to 19th century mathematicians. In his research, Gadi had discovered simple and elegant proofs of the above mention...

In the classical firing squad problem, an unknown number of nodes represented by identical finite states machines is arranged on a line and in each time unit each node may change its state according to its neighbors' states. Initially all nodes are passive, except one specific node located at an end of the line, which issues a fire command. This co...

In the stabilizing consensus problem, each agent of a networked system has an input value and is repeatedly writing an output value; it is required that eventually all the output values stabilize to the same value which, moreover, must be one of the input values. We study this problem for a synchronous model with identical and anonymous agents that...

Distance-based methods for phylogenetic reconstruction are based on a two-step approach: first, pairwise distances are computed from DNA sequences associated with a given set of taxa, and then these distances are used to reconstruct the phylogenetic relationships between taxa. Because the estimated distances are based on finite sequences, they are...

In this article, we study algorithms for dynamic networks with asynchronous start, i.e., each node may start running the algorithm in a different round. Inactive nodes transmit only heartbeats, which contain no information but can be detected by active nodes. We make no assumption on the way the nodes are awakened, except that for each node u there...

We present rumor spreading protocols for the complete graph topology that are robust against an arbitrary number of adversarial initial node failures. Our protocols are the first rumor spreading protocols combining the following three properties: they can tolerate any number of failures, they distribute the rumor to all nodes using linear number of...

Background Distance-based phylogenetic reconstruction methods use evolutionary distances between species in order to reconstruct the phylogenetic tree spanning them. There are many different methods for estimating distances from sequence data. These methods assume different substitution models and have different statistical properties. Since the tr...

Phylogenetic reconstruction methods attempt to reconstruct a tree describing the evolution of a given set of species using sequences of characters (e.g. DNA) extracted from these species as input. A central goal in this area is to design algorithms which guarantee reliable reconstruction of the tree from short input sequences, assuming common stoch...

A coloring of a graph is convex if the vertices that pertain to any color induce a connected subgraph; a partial coloring (which assigns colors to a subset of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring has applications in fields such as phylogenetics, communication or transportation networks, etc. W...

Distance-based phylogenetic reconstruction methods use the evolutionary distances between species in order to reconstruct the tree spanning them. The evolutionary distance between two species, which is computed from their DNA (or protein) sequences, is typically considered as a fixed function of these sequences, predetermined by the assumed model o...

Distance based reconstruction methods of phylogenetic trees consist of two independent parts: first, inter-species distances are inferred assuming some stochastic model of sequence evolution; then the inferred distances are used to construct a tree. In this paper we concentrate on the task of inter-species distance estimation. Specifically, we char...

We consider a failure-free, asynchronous message passing network with n links, where the processors are arranged on a ring or a chain. The processors are identically programmed but have distinct identities, taken from {0, 1,… , M − 1}. We investigate the communication costs of three well studied tasks: Consensus, Leader, and MaxF (finding the maxim...

Phylogenetic reconstruction is the problem of reconstruct- ing an evolutionary tree from sequences corresponding to leaves of that tree. A central goal in phylogenetic recon- struction is to be able to reconstruct the tree as accurately as possible from as short as possible input sequences. The se- quence length required for correct topological rec...

In this work we consider hierarchical clustering algorithms, such as UPGMA, which follow the closest-pair joining scheme. We study opti- mal O(n2)-time implementations of such algorithms which use a 'locally closest' joining scheme, and specify conditions under which this relaxed joining scheme is equivalent to the original one (i.e. 'globally clos...

This work considers the problem of reconstructing a phylogenetic tree from triplet-dissimilarities, which are dissimilarities defined over taxon-triplets. Triplet-dissimilarities are possibly the simplest generalization of pairwise dissimilarities, and were used for phylogenetic reconstructions in the past few years. We study the hardness of findin...

A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring of trees arises in areas such as phylogenetics, linguistics, etc. e.g., a perfect phylogenetic tree is o...

Reconstructing phylogenetic trees efficiently and accurately from distance estimates is an ongoing challenge in computational biology from both practical and theoretical considerations. We study algorithms which are based on a characterization of edge-weighted trees by distances to LCAs (Least Common Ancestors). This characterization enables a dire...

We prove that the problem of determining the minimum propositional proof length is NP-hard to approximate within any constant factor. These results hold for all Frege systems, for all extended Frege systems, for resolution and Horn resolution, and for the sequent calculus and the cut-free sequent calculus. Also, if NP is not in QP = DTIME(nlogO(1)...

Linear Interval Routing is a space-efficient routing method for point-to-point communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wrap-around. It was noted in [BLT91] that not every network has a valid Linear Interval Labeling Scheme (LILS)....

We focus on unreliable asynchronous shared memory model which support only atomic read and write operations. For such a model we provide a necessary condition for the solvability of problems in the precence of multiple undetectable crash failures. Also, by using game-theoretical notions, a necessary and sufficient condition is provided, for the sol...

A.C. Yao proved that in the decision-tree model the average complexity of the best deterministic algorithm is a lower bound on the complexity of randomized algorithms that solve the same problem. Here it is shown that a similar result does not always hold in the common model of distributed computation, the model in which all the processors run the...

A distributed task T is 1-solvable if there exists a protocol that solves it in the presence of (at most) one crash failure. A precise characterization of the 1-solvable tasks was given in [BMZ]. In this paper we determine the number of rounds of communication that are required, in the worst case, by a protocol which 1-solves a given 1-solvable tas...

A unified and general framework for the study of nondeterministic polynomial optimization problems (NPOP) is presented and some properties of NPOP's are investigated. A characterization of NPOP's with regard to their approximability properties is given by proving necessary and sufficient conditions for two approximability schemes. Known approximabi...

Link structure analysis is widely recognized as an important tool in WWW information retrieval and is extensively used in the retrieval and ranking algorithms of major WWW search engines. Common extensions of link analyses involve changing the Web subgraphs that are analyzed. In this work, we present two techniques which bias co‐citation based link...

Supertree methods are used to construct a large tree over a large set of taxa, from a set of small trees over overlapping subsets of the complete taxa set. Since accurate reconstruction methods are currently limited to a maximum of few dozens of taxa, the use of a supertree method in order to construct the tree of life is inevitable. Supertree meth...

A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex coloring of trees arise in areas such as phylogenetics, linguistics, etc. eg, a perfect phylogenetic tree is one...

Web search algorithms that rank Web pages by examining the link structure of the Web are attractive from both theoretical and practical aspects. Today’s prevailing link-based ranking algorithms rank Web pages by using the dominant eigenvector of certain matrices—like the co-citation matrix or variations thereof. Recent analyses of ranking algorithm...

A coloring of a tree is convex if the vertices that pertain to any color induce a connected subtree; a partial coloring (which assigns colors to some of the vertices) is convex if it can be completed to a convex (total) coloring. Convex colorings of trees arise in areas such as phylogenetics, linguistics, etc., e.g., a perfect phylogenetic tree is...

We study the problem of caching query result pages in Web search engines. Popular search engines receive millions of queries per day, and for each query, return a result page to the user who submitted the query. The user may request additional result pages for the same query, submit a new query, or quit searching altogether. An efficient scheme for...

We study the process in which search engines with segmented indices serve queries. In particular, we investigate the number of result pages that search engines should prepare during the query processing phase.Search engine users have been observed to browse through very few pages of results for queries that they submit. This behavior of users sugge...

Large-scale Web search engines currently index billions of Web documents. These enormous indices are often distributed across multiple index segment. One common architecture partitions the docu-ment set into several disjoint subsets, indexing each subset on a separate machine (index segment). When answering queries, the architecture requires execut...

We continue the study of communication costs of Consensus and Leader initiated in a previous paper. We deal with all scenarios with linear complexity in a tree topology, and prove exact (as opposed to asymptotic) tight bounds for the bit and message complexities. A particular scenario depends on whether the tree size or the size parity is known to...

We study the caching of query result pages in Web search engines. Popular search engines receive millions of queries per day, and efficient policies for caching query results may enable them to lower their response time and reduce their hardware requirements. We present PDC (probability driven cache), a novel scheme tailored for caching search resu...

A public data structure is required to work correctly in a concurrent environment where many processes may try to access it, possibly at the same time. In implementing such a structure nothing can be assumed in advance about the number or the identities of the processes that might access it.While most of the known concurrent data structures are not...

Interval Routing is a routing method that was proposed in order to reduce the size of the routing tables by using intervals and was extensively studied and implemented. Some variants of the original method were also defined and studied. The question of characterizing networks which support optimal (i.e., shortest path) Interval Routing has been tho...

We prove that the problem of determining the minimum propositional proof length is NPhard to approximate within a factor of 2 log 1-o(1) n . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the polynomial calculus, the sequent calculu...

This paper studies the design of low-cost survivable wavelength-division-multiplexing (WDM) networks. To achieve survivability, lightpaths are arranged as a set of rings. Arrangement in rings is also necessary to support SONET/SDH protection schemes such as 4FBLSR above the optical layer. This is expected to be the most common architecture in regio...

We study the process in which search engines with segmented indices serve queries. In particular, we investigate the number of result pages that search engines should prepare during the query processing phase. Search engine users have been observed to browse through very few pages of results for queries that they submit. This behavior of users sugg...

The distributed bit complexity of an asynchronous network of processors is a lower bound on the worst case bit complexity of computing any non-constant function of the inputs to the processors [MW]. This concept attempts to capture the amount of communication required for any "useful" computation on the network.

Today, when searching for information on the WWW, one usually performs a query through a term-based search engine. These engines return, as the query's result, a list of Web pages whose contents matches the query. For broad-topic queries, such searches often result in a huge set of retrieved documents, many of which are irrelevant to the user. Howe...

We prove that the problem of determining the minimum propositional proof length is NP-hard to approximate within any constant factor. These results hold for all Frege systems, for all extended Frege systems, for resolution and Horn resolution, and for the sequent calculus and the cut-free sequent calculus. Also, if NP is not in QP = DTIME(n log O(1...

We are motivated by the developments in all-optical networks - a new tech- nology that supports high bandwidth demands. These networks provide a set of ligthpaths which can be seen as high-bandwidth pipes on which communication is performed. Since the capacity enabled by this technology substatially exceeds the one provided by conventional networks...

We study connection networks in which certain pairs of nodes have to be connected by k edge-disjoint paths, and study bounds for the minimal sum of lengths of such k paths. We define the related notions of totalk-distance for a pair of nodes and totalk-diameter of a connection network, and study the value TDk(d) which is the maximal such totalk-dia...

We present a simple and efficient method for constructing sparse decompositions of networks. This method is used to construct the sparse decompositions needed for variants of the synchronizers in [2,15] in time and communication complexities, while maintaining constant messages size and constant memory per edge. Using these decompositions, we prese...

Today, when searching for information on the World Wide Web, one usually performs a query through a term-based search engine. These engines return, as the query's result, a list of Web sites whose contents match the query. For broad topic queries, such searches often result in a huge set of retrieved documents, many of which are irrelevant to the u...

Linear interval routing is a space-efficient routing method for point-to-point communication networks. It is a restricted variant of interval routing where the routing range associated with every link is represented by an interval with no wraparound. A common way to measure the efficiency of such routing methods is in terms of the maximal length of...

Yem DinitzShlomo MoranSergio RajsbaumAbstractWe consider a failure-free, asynchronous message passingnetwork, with n processors arranged on a ring or a chain.The processes are identically programmed but have distinctidentities, taken from f1; : : : ; Mg. We investigate the communicationcosts of three well studied tasks: Consensus,Leader, and MaxF (...

In the totally anonymous shared memory model of asynchronous distributed computing, processes have no id's and run identical programs. Moreover, processes have identical interface to the shared memory, and in particular, there are no single-writer registers. This paper assumes that processes do not fail, and the shared memory consists only of read/...

A counting protocol (mod m) consists of shared memory bits—referred to as the counter—and of a procedure for incrementing the counter value by 1 (mod m). The procedure may be executed by many processes concurrently. It is required to satisfy a very weak correctness requirement; namely, the counter is required to show a correct value only in quiesce...

We study connection networks in which certain pairs of nodes have to be connected by k edge-disjoint paths, and study bounds for the minimal sum of lengths of such k paths. We define the related notions of total/sub k/-distance for a pair of nodes and total/sub k/-diameter of a connection network, and study the value TD/sub k/(d) which is the maxim...

A distributed system is self-stabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The self-stabilization property makes the system tolerant to faults in which processors exhibit a faulty behavior for a while and then recover spontaneously...

We study a new problem, the wakeup problem, that seems to be very fundamental in distributed computing. We present efficient solutions to the problem and show how these solutions can be used to solve the consensus problem, the leader election problem, and other related problems. The main question we try to answer is, how much memory is needed to so...

A.C. Yao proved that in the decision-tree model the average complexity of the best deterministic algorithm is a lower bound on the complexity of randomized algorithms that solve the same problem. Here it is shown that a similar result does not always hold in the common model of distributed computation, the model in which all the processors run the...

Linear Interval Routing is a space-efficient routing method for point-to-point communication networks. It is a restricted variant of Interval Routing where the routing range associated with every link is represented by an interval with no wrap-around. A common way to measure the efficiency of such routing methods is in terms of the maximal length o...

In this paper we study implementations of concurrent counters, which count modulo some (large) integerm, using only small valued objects. A concurrent counter is a counter that can be incremented and read, possibly at the same time, by many processes. The counters we study do not depend on the initial state of the memory and hence are more robust t...

We define and study public data structures, which are concurrent data structures in the shared memory environment, which enable access to an unknown (and possibly infinite) set of identical processes. Specific cases of such data structures (like counting networks and concurrent counters) have been studied recently, and such data structures seem to...

We introduce an N-process deterministic concurrent object for N ≥ 3 processes, called the conditional consensus object. This object, denoted as W, is hard-wired in the sense that each process P can access it using a single fixed port (though P can use different ports in different copies of W). We prove that W satisfies the following properties: The...

) Abstract A self-stabilizing system is a distributed system which can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of an outside intervention. The self-stabilization property is very useful for systems in which processors may crash and then recover spontaneously in an arbitrar...

A distributed system is self-stabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The self-stabilization property makes the system tolerant to faults in which processors crash and then recover spontaneously in an arbitrary state. When the...

A distributed task T is 1-solvable if there exists a protocol that solves it in the presence of (at most) one crash failure. A precise characterization of the 1-solvable tasks was given by Biran et al. (1990). In this paper we determine the number of rounds of communication that are required, in the worst case, by a protocol which 1-solves a given...

Analyzing distributed protocols in various models often involves a careful analysis of the set ofadmissible runs, for which the protocols should behave correctly. In particular, the admissible runs assumed by at-resilient protocol are runs which are fair for all but at mostt processors. In this paper we defineclosed sets of runs, and suggest a tech...

We introduce a novel technique, the scheduler luck game (in short sl-game) for analyzing the performance of randomized distributed protocols. We apply it in studying uniform self-stabilizing protocols for leader election under read/write atomicity. We present two protocols for the case where each processor in the system can communicate with all oth...

Self-stabilizing message driven protocols are defined and discussed. The class weakexclusion that contains many natural tasks such as `-exclusion and token-passing is defined, and it is shown that in any execution of any self-stabilizing protocol for a task in this class, the configuration size must grow at least in a logarithmic rate. This last lo...

A distributed system is self-stabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The self-stabilization property makes the system tolerant to faults in which processors crash and then recover spontaneously in an arbitrary state. When the...

A public data structure is required to work correctly in a concurrent environment where many processes may try to access it, possibly at the same time. In implementing such a structure nothing can be assumed in advance about the number or the identities of the processes that might access it. While most of the known concurrent data structures are no...

A distributed task for n processes is defined by a decision mapping, which maps each input vector to a set of “correct” decision vectors. For an integer t, the t-solvability problem is the problem of deciding from the specification of a distributed task T whether T can be solved in a completely asynchronous environment in the presence of at most t...

Let the consensus number of a given set \(\mathcal{S}\) of shared objects, denoted \(\mathcal{C}\mathcal{N}(\mathcal{S})\), be the maximum number n such that there is a wait-free consensus protocol for n distinct processes, which communicate only by accessing objects in \(\mathcal{S}\). An interesting question concerning consensus numbers is the fo...

We investigate the impossibility of solving certain problems in an unreliable distributed system where multiple processes may,fail. We assume undetectable crash failures which means that a process may become,faulty at any time during an execution and that no event can happen on a process after it fails. A sucient,condition is provided for the unsol...

In Moran and Warmuth (1993, SIAM .J. Comput.22, No. 2, 379-399), it was shown that computing any non-constant function on a ring of n of processors requires Ω(n log) bits and this bound is tight. This model assumed that all the processors in the ring are identical (anonymous), i.e., all processors run the same program and the only parameter of the...

Ad-scheduling of a graphG is a sequence of rounds, each consisting of some of the nodes of the graph, such that the distance between any two nodes participating in the same round is greater thand. Ad-scheduler is a protocol that determines ad-scheduling ofG. A 1-scheduler is applicable to process scheduling in a resource-sharing system, and to prop...

We study the VLSI-related problem of embedding graphs in books. A book embedding of a graph G=(V,E) consists of two parts, namely, (1) an ordering of V along the spine of the book, and (2) an assignment of each eϵE to a page of the book, so that edges assigned to the same page do not intersect. In devising an embedding, one seeks to minimize the nu...

We study the consensus problem in a shared memory model where all processes are programmed alike, there is no global synchronization, it is not possible to simultaneously reset all parts of the system to a known initial state, and processes may be faulty. We present a consensus protocol for n processes which can tolerate up to ⌈n/2⌉ − 1 failures an...

We consider two versions of a game for two players, A and B. The game consists of manipulations of words of length n over an alphabet of size σ, for arbitrary n and σ. For σ = 2 the game is described as follows: initially, player A puts n drinking glasses on a round table, some of which are upside down. Player B attempts to force player A to set al...

Three self-stabilizing protocols for distributed systems in the shared memory model are presented. The first protocol is a mutual-exclusion prootocol for tree structured systems. The second protocol is a spanning tree protocol for systems with any connected communication graph. The thrid protocol is obtianed by use offair protoco combination, a sim...

Abstract A counting protocol (mod m) consists of shared memory,bits - referred to as the counter - and of a procedure for incrementing the counter value by 1 (mod m). The procedure may be executed by many processes concurrently. It is required to satisfy a very weak correctness requirement, namely: the counter is required to show a correct value on...

Analyzing distributed protocols in various models often involves a careful analysis of the set of admissible runs, for which the protocols should behave correctly. In particular, the admissible runs assumed by a t-resilient protocol are runs which are fair for all but at most t processors. In this paper we define closed sets of runs, and suggest a...

An ongoing debate among theoreticians of distributed systems concerns the global time issue. The basic question seems to be to what extent does a model with global time reeect the 'real' behavior of a distributed system. The assumption of the existence of global time simpliies the analysis of distributed algorithms to an extent that makes it almost...

p>A distributed task T is 1-solvable if there exists a protocol that solves it in the presence of (at most) one crash failure. A precise characterization of the 1-solvable tasks was given by the authors in 1990. In this paper we determine the number of rounds of communication that are required, in the worst case, by a protocol which 1-solves a giv...

An ongoing debate among theoreticians of distributed systems concerns the global time issue. The basic question seems to be to what extent does a model with global time reflect the ‘real’ behavior of a distributed system. The assumption of the existence of global time simplifies the analysis of distributed algorithms to an extent that makes it almo...

A distributed system is selfstabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of an outside intervention. The self-stabilization property makes the system tolerant to faults in which processors crash and then recover spontaneously in an arbitrary state. When th...