C. Dwork, M. Herlihy, Serge A. Plotkin, Orli Waarts
{"title":"Time-Lapse Snapshots","authors":"C. Dwork, M. Herlihy, Serge A. Plotkin, Orli Waarts","doi":"10.1137/S0097539793243685","DOIUrl":"https://doi.org/10.1137/S0097539793243685","url":null,"abstract":"Abstract. A snapshot scan algorithm takes an \"instantaneous\" picture of a region of shared memory that may he updated by concurrent processes. Many complex shared memory algorithms can be greatly simplified by structuring them around the snapshot scan abstraction. Unforinnately, the substantial decrease in conceptual complity is quite often counterbalanced by an increase in computational complexity. In this paper, we introduce the notion of a weak snapshot scan, a slightly weaker primitive that has a more efficient implementation. We propose the following methodology for using this abstraction: first, design and verify an algorithm using the more powerful snapshot scan, and second, replace the more powerful but less efficient snapshot with the weaker but more efficient snapshot, and show that the weaker abstraction nevertheless suffices to ensure the correctness of the enclosing algorithm. We give two examples of algorithms whose performance can be enhanced while retaining a simple modular structure: bounded concurrent timestamping, and bounded randomized consensus. The resulting timestamping protocol is the fastest known bounded concurrent timestamping protocol. The resulting randomized consensus protocol matches the computational complexity of the best known protocol that uses only bouned values.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1992-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132831474","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":"Full Abstraction and the Context Lemma","authors":"T. Jim, A. Meyer","doi":"10.1137/S0097539791224212","DOIUrl":"https://doi.org/10.1137/S0097539791224212","url":null,"abstract":"It is impossible to add a combinator to PCF to achieve full abstraction for models such as Berry''s stable domains in a way analogous to the addition of the \"parallel-or\" combinator that achieves full abstraction for the familiar cpo model. In particular, we define a general notion of rewriting system of the kind used for evaluating simply typed l-terms in Scott''s PCF. Any simply type l-calculus with such a \"PCF-like\" rewriting semantics is shown necessarily to satisfy Milner''s Context Lemma. A simple argument demonstrates that any denotational semantics that is adequate for PCF, and in which certain simple Boolean functionals exist, cannot be fully abstract for any extension of PCF satisfying the Context Lemma. An immediate corollary is that stable domains cannot be fully abstract for any extension of PCF definable by PCF-like rules.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129196118","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":"An Optimal Algorithm for Computing Visibility in the Plane","authors":"P. Heffernan, Joseph S. B. Mitchell","doi":"10.1137/S0097539791221505","DOIUrl":"https://doi.org/10.1137/S0097539791221505","url":null,"abstract":"We give an algorithm to compute the visibility polygon from a point among a set of h pairwise-disjoint polygonal obstacles with a total of n vertices. Our algorithm uses O(n) space and runs in optimal time Θ(n+hlog h), improving the previous upper bound of O(n log h).","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132969537","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":"On the Zone Theorem for Hyperplane Arrangements","authors":"H. Edelsbrunner, R. Seidel, M. Sharir","doi":"10.1137/0222031","DOIUrl":"https://doi.org/10.1137/0222031","url":null,"abstract":"The zone theorem for an arrangement of n hyperplanes in d-dimensional real space says that the total number of faces bounding the cells intersected by another hyperplane is $O(n^{d - 1} )$. This result is the basis of a time-optimal incremental algorithm that constructs a hyperplane arrangement and has a host of other algorithmic and combinatorial applications. Unfortunately, the original proof of the zone theorem, for $d geqslant 3$, turned out to contain a serious and irreparable error. This paper presents a new proof of the theorem. The proof is based on an inductive argument, which also applies in the case of pseudohyperplane arrangements. The fallacies of the old proof along with some ways of partially saving that approach are briefly discussed.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129413499","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":"An Almost Linear-Time Algorithm for the Dense Subset-Sum Problem","authors":"Z. Galil, Oded Margalit","doi":"10.1137/0220072","DOIUrl":"https://doi.org/10.1137/0220072","url":null,"abstract":"This paper describes a new approach for solving a large subproblem of the subset-sum problem. It is useful for solving other NP-hard integer programming problems. The limits and potential of this approach are investigated.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132149497","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":"Greedy Packet Scheduling","authors":"I. Cidon, S. Kutten, Y. Mansour, D. Peleg","doi":"10.1137/S0097539791217695","DOIUrl":"https://doi.org/10.1137/S0097539791217695","url":null,"abstract":"Scheduling packets to be forwarded over a link is an important subtask of the routing process both in parallel computing and in communication networks. This paper investigates the simple class of greedy scheduling algorithms, namely, algorithms that always forward a packet if they can. It is first proved that for various “natural” classes of routes, the time required to complete the transmission of a set of packets is bounded by the sum of the number of packets and the maximal route length, for any greedy algorithm (including the arbitrary scheduling policy). Next, tight time bounds of Θ(n) are proved for a specific greedy algorithm on the class of shortest paths in n-vertex networks. Finally it is shown that when the routes are arbitrary, the time achieved by various “natural” greedy algorithms can be as bad as Ω(n1.5), when O(n) packets have to be forwarded on an n-vertex network.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129254988","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":"Selection Networks","authors":"N. Pippenger","doi":"10.1137/0220054","DOIUrl":"https://doi.org/10.1137/0220054","url":null,"abstract":"An upper bound asymptotic to 2n log n is established for the number of comparators required in a network that classifies n values into two classes, each containing n/2 values, with each value in one class less than or equal to each value in the other. (The best lower bound known for this problem is asymptotic to (n/2) log2 n.) Key words, comparator, classifier, expanding graph, random walk AMS(MOS) subject classifications. 68E05, 94C10","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128746657","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":"Computing Puiseux-Series Solutions to Determinantal Equations via Combinatorial Relaxation","authors":"K. Murota","doi":"10.1137/0219077","DOIUrl":"https://doi.org/10.1137/0219077","url":null,"abstract":"Let $A(t,x) = (A_{ij} (t,x))$ be a square matrix with $A_{ij}$ being a polynomial in t and x. This paper proposes an algorithm for computing the Puiseux (= fractional power) series solutions $x = x(t)$ to the equation ${operatorname{det}}A(t, x) = 0$. The algorithm is based on an observation which links the Newton diagram (polygon) for det ${operatorname{det}}A(t, x)$ with the perfect matchings of a bipartite graph associated with A. The algorithm is efficient, making full use of available fast network-type algorithms.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"46 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1990-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133109589","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":"An Improved Algorithm for Approximate String Matching","authors":"Z. Galil, Kunsoo Park","doi":"10.1137/0219067","DOIUrl":"https://doi.org/10.1137/0219067","url":null,"abstract":"Given a text string, a pattern string, and an integer k, a new algorithm for finding all occurrences of the pattern string in the text string with at most k differences is presented. Both its theoretical and practical variants improve the known algorithms.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122048463","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":"Complete Problems and Strong Polynomial Reducibilities","authors":"K. Ganesan, S. Homer","doi":"10.1137/0221044","DOIUrl":"https://doi.org/10.1137/0221044","url":null,"abstract":"A set A is m-reducible to a set B if and only if there is a polynomial-time computable function f such that for all x, $x in A Leftrightarrow f(x) in B$. A set C is m-complete for a class S if $C in S$ and all sets in S are m-reducible to C. One-reducibility and one-completeness can be defined by requiring f to be one–one. Two sets A and B are p-isomorphic if the function f can be taken one-to-one, onto, and polynomially invertible. In this paper it is shown that all the m-complete sets are one–one complete for ${operatorname{DTIME}}(2^{mathcal{O}(n)} )$, ${operatorname{NTIME}}(2^{mathcal{O}(n)} )$, and the class of recursively enumerable sets. Further, all the sets complete for ${operatorname{NTIME}}(2^{mathcal{O}(n)} )$ under 1–L (or two-way DFA) reductions are p-isomorphic. All the m-complete sets for ${operatorname{DTIME}}(2^{mathcal{O}(n)} )$ are p-isomorphic if and only if all the m-complete sets for DTIME($2^{{text{poly}}} $) are p-isomorphic.","PeriodicalId":160227,"journal":{"name":"SIAM journal on computing (Print)","volume":"105 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1989-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127151121","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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