J. Bermond, L. Gargano, A. A. Rescigno, U. Vaccaro
{"title":"Fast Gossiping by Short Messages","authors":"J. Bermond, L. Gargano, A. A. Rescigno, U. Vaccaro","doi":"10.1137/S0097539795283619","DOIUrl":"https://doi.org/10.1137/S0097539795283619","url":null,"abstract":"Gossiping is the process of information diffusion in which each node of a network holds a packet that must be communicated to all other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a fixed number p of packets at each round. In the first part of the paper we study the extremal case p = 1 and we exactly determine the optimal number of communication rounds to perform gossiping for several classes of graphs, including Hamiltonian graphs and complete k-ary trees. For arbitrary graphs we give asymptotically matching upper and lower bounds. We also study the case of arbitrary p and we exactly determine the optimal number of communication rounds to perform gossiping under this hypothesis for complete graphs, hypercubes, rings, and paths.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122207348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Average and Randomized Complexity of Distributed Problems","authors":"Nechama Allenberg-Navony, A. Itai, S. Moran","doi":"10.1137/S0097539793252432","DOIUrl":"https://doi.org/10.1137/S0097539793252432","url":null,"abstract":"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 same program (that may depend on the processors' input).","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121823629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Maximum Latency and Identification of Positive Boolean Functions","authors":"K. Makino, T. Ibaraki","doi":"10.1137/S0097539794276324","DOIUrl":"https://doi.org/10.1137/S0097539794276324","url":null,"abstract":"Consider the problem of identifying min T(f) and max F(f) of a positive (i.e., monotone) Boolean function f, by using membership queries only, where min T(f) (maxF(f)) denotes the set of minimal true vectors (maximal false vectors) of f. It is known that an incrementally polynomial algorithm exists if and only if there is a polynomial time algorithm to check the existence of an unknown vector for given sets MT(subseteq ) min T(f) and MF(subseteq ) max F(f). Unfortunately, however, the complexity of this problem is still unknown. To answer this question partially, we introduce in this paper a measure for the difficulty of finding an unknown vector, which is called the maximum latency. If the maximum latency is constant, then an unknown vector can be found in polynomial time and there is an incrementally polynomial algorithm for identification. Several subclasses of positive functions are shown to have constant maximum latency, e.g., 2-monotonic positive functions, Δ-partial positive threshold functions and matroid functions, while the class of general positive functions has maximum latency not smaller than [n/4]+1 and the class of positive k-DNF functions has Ω(√n) maximum latency.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1994-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122443889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
P. Bertolazzi, G. Battista, C. Mannino, R. Tamassia
{"title":"Optimal Upward Planarity Testing of Single-Source Digraphs","authors":"P. Bertolazzi, G. Battista, C. Mannino, R. Tamassia","doi":"10.1137/S0097539794279626","DOIUrl":"https://doi.org/10.1137/S0097539794279626","url":null,"abstract":"A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in software engineering, project management, and visual languages. In this paper we investigate upward planarity testing of single-source digraphs: we provide a new combinatorial characterization of upward planarity, and give an optimal algorithm for upward planarity testing. Our algorithm tests whether a single-source digraph with $n$ vertices is upward planar in $O(n)$ sequential time, and in $O(log n)$ time on a CRCW PRAM with $n loglog n / log n$ processors, using $O(n)$ space. The algorithm also constructs an upward planar drawing if the test is successful. The previous best result is an $O(n^2)$-time algorithm by Hutton and Lubiw. No efficient parallel algorithms for upward planarity testing were previously known.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"135 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121976099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tree Reconstruction from Partial Orders","authors":"Sampath Kannan, T. Warnow","doi":"10.1137/S0097539793252195","DOIUrl":"https://doi.org/10.1137/S0097539793252195","url":null,"abstract":"The problem of constructing trees given a matrix of interleaf distances is motivated by applications in computational evolutionary biology and linguistics. The general problem is to find an edge-weighted tree which most closely approximates (under some norm) the distance matrix. Although the construction problem is easy when the tree exactly fits the distance matrix, optimization problems under all popular criteria are either known or conjectured to be NP-complete. In this paper we consider the related problem where we are given a partial order on the pairwise distances, and wish to construct (if possible) an edge-weighted tree realizing the partial order. In particular we are interested in partial orders which arise from experiments on triples of species. We will show that the consistency problem is NP-hard in general, but that for certain special cases the construction problem can be solved in polynomial time.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"49 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113960794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Complexity of Processing Hierarchical Specifications","authors":"D. Rosenkrantz, H. Hunt","doi":"10.1137/0222042","DOIUrl":"https://doi.org/10.1137/0222042","url":null,"abstract":"Hierarchical object descriptions consisting of a set of module descriptions are considered, where each module is either a primitive module or has a body that is an interconnection of submodules. The description represents a flattened object, whose size can be exponential in the size of the description. The complexity of processing and/or analyzing such hierarchically specified objects is considered. The simulation of hierarchically specified circuits is emphasized, but the results are applicable to other kinds of hierarchically specified objects.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"156 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127361234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A First-Order Isomorphism Theorem","authors":"E. Allender, J. Balcázar, N. Immerman","doi":"10.1137/S0097539794270236","DOIUrl":"https://doi.org/10.1137/S0097539794270236","url":null,"abstract":"We show that for most complexity classes of interest, all sets complete under first-order projections are isomorphic under first-order isomorphisms. That is, a very restricted version of the Berman-Hartmanis Conjecture holds.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"103 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1993-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116047124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Subexponential Algorithm for Abstract Optimization Problems","authors":"B. Gärtner","doi":"10.1137/S0097539793250287","DOIUrl":"https://doi.org/10.1137/S0097539793250287","url":null,"abstract":"An abstract optimization problem (AOP) is a triple $(H,<, Phi)$ where $H$ is a finite set, $<$ a total order on $2^{H}$ and $Phi$ an oracle that, for given $Fsubseteq Gsubseteq H$, either reports that $F=min_{<}{F'mid F'subseteq G}$ or returns a set $F'subseteq G$ with $F' $$e^{2sqrt{n}+O(sqrt[4]{n}ln n)}$$ oracle calls, $n=|H|$. In contrast, any deterministic algorithm needs to make $2^{n}-1$ oracle calls in the worst case. \u0000The algorithm is applied to the problem of finding the distance between two $n$-vertex (or $n$-facet) convex polyhedra in $d$-space, and to the computation of the smallest ball containing $n$ points in $d$-space; for both problems we give the first subexponential bounds in the arithmetic model of computation.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133351376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Increasing the Size of a Network by a Constant Factor can Increase Performance by more than a Constant Factor","authors":"R. Koch","doi":"10.1137/0221048","DOIUrl":"https://doi.org/10.1137/0221048","url":null,"abstract":"The performance of unbuffered routing algorithms for parallel computer architectures is analyzed. Unbuffered algorithms are an alternative to the use of queues. When the capacity of a switch or communications link is exceeded, the extra messages are discarded, and another attempt to transmit the message will be made at a later time. The analysis presented here is relevant for routing on the BBN Butterfly and Agarwal and Knight’s Alewife architecture, both of which have interconnection networks based on the butterfly graph.Suppose that each of the N inputs of the butterfly independently decides to send a message with probability p, and that the message is sent to a random output, with each output having an equal probability of being chosen. If more than q messages attempt to traverse an edge, the extra messages over q are discarded. q is called the dilation of the network. The bandwidth is the number of messages that reach their destinations. It is shown that if $p = Omega ((log N)^{ - 1/q} )$, the expec...","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"265 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114272135","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"New Resultant Inequalities and Complex Polynomial Factorization","authors":"V. Pan","doi":"10.1137/S0097539792235712","DOIUrl":"https://doi.org/10.1137/S0097539792235712","url":null,"abstract":"We deduce some new probabilistic estimates on the distances between the zeros of a polynomial p(x) by using some properties of the discriminant of p(x) and apply these estimates to improve the fastest deterministic algorithm for approximating polynomial factorization over the complex field. Namely, given a natural n, positive e, such that log(1/e)=O(n log n), and the complex coefficients of a polynomial p(x) = Σ i=0 n pixi, such that Pn ≠ 0, ∑i¦pi¦≤1, we compute (within the error norm e) a factorization of p(x) as a product of factors of degrees at most n/2, by using O(log2n) time and n3 processors under the PRAM arithmetic model of parallel computing or by using O(n2 log2n) arithmetic operations. The algorithm is randomized, of Las Vegas type, allowing a failure with a probability at most δ, for any positive δ < 1 such that log(1/δ)=O(log n). Except for a narrow class of polynomials p(x), these results can be also obtained for e such that log(1/e)=O(n2 log n).","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"106 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126992592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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