Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185389
B. Kapron, S. Cook
A. Cobham (1964) presented a machine-independent characterization of computational feasibility, via inductive definition. R. Constable (1973) was apparently the first to consider the notion of feasibility for type 2 functionals. K. Mehlhorn's (1976) study of feasible reducibilities proceeds from Constable's work. Here, a class of polytime operators is defined, using a generalization of Cobham's definition. The authors provide an affirmative answer to the question of whether there is a natural machine based definition of Mehlhorn's class.<>
a . Cobham(1964)通过归纳定义提出了与机器无关的计算可行性表征。康斯特布尔(1973)显然是第一个考虑二类泛函的可行性的人。K. Mehlhorn(1976)对可行可约性的研究源于Constable的工作。在这里，使用Cobham定义的推广定义了一类多时算子。对于Mehlhorn的类是否存在一个自然的基于机器的定义这个问题，作者提供了一个肯定的答案。
{"title":"A new characterization of Mehlhorn's polynomial time functionals","authors":"B. Kapron, S. Cook","doi":"10.1109/SFCS.1991.185389","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185389","url":null,"abstract":"A. Cobham (1964) presented a machine-independent characterization of computational feasibility, via inductive definition. R. Constable (1973) was apparently the first to consider the notion of feasibility for type 2 functionals. K. Mehlhorn's (1976) study of feasible reducibilities proceeds from Constable's work. Here, a class of polytime operators is defined, using a generalization of Cobham's definition. The authors provide an affirmative answer to the question of whether there is a natural machine based definition of Mehlhorn's class.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122321056","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185402
D. Du, Yanjun Zhang, Qing Feng
Finding a shortest network interconnecting a given set of points in the Euclidean plane (a Steiner minimum tree) is known to be NP-hard. It is shown that there exists a polynomial-time heuristic with a performance ratio bigger than square root 3/2.<>
{"title":"On better heuristic for Euclidean Steiner minimum trees","authors":"D. Du, Yanjun Zhang, Qing Feng","doi":"10.1109/SFCS.1991.185402","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185402","url":null,"abstract":"Finding a shortest network interconnecting a given set of points in the Euclidean plane (a Steiner minimum tree) is known to be NP-hard. It is shown that there exists a polynomial-time heuristic with a performance ratio bigger than square root 3/2.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126064438","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185347
J. Matoušek, Nathaly Miller, J. Pach, M. Sharir, Shmuel Sifrony, E. Welzl
It is shown that for every fixed delta >0 the following holds: if F is a union of n triangles, all of whose angles are at least delta , then the complement of F has O(n) connected components, and the boundary of F consists of O(n log log n) segments. This latter complexity becomes linear if all triangles are of roughly the same size or if they are all infinite wedges. A randomized algorithm that computes F in expected time O(n2/sup alpha (n)/ log n) is given. Several applications of these results are presented.<>
{"title":"Fat triangles determine linearly many holes (computational geometry)","authors":"J. Matoušek, Nathaly Miller, J. Pach, M. Sharir, Shmuel Sifrony, E. Welzl","doi":"10.1109/SFCS.1991.185347","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185347","url":null,"abstract":"It is shown that for every fixed delta >0 the following holds: if F is a union of n triangles, all of whose angles are at least delta , then the complement of F has O(n) connected components, and the boundary of F consists of O(n log log n) segments. This latter complexity becomes linear if all triangles are of roughly the same size or if they are all infinite wedges. A randomized algorithm that computes F in expected time O(n2/sup alpha (n)/ log n) is given. Several applications of these results are presented.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"9 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116673637","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185435
Ming-Deh A. Huang, D. Ierardi
Several computational problems concerning the construction of rational functions and intersecting curves over a given curve are studied. The first problem is to construct a rational function with prescribed zeros and poles over a given curve. More precisely, let C be a smooth projective curve and assume as given an affine plane model F(x,y)=0 for C, a finite set of points P/sub i/=(X/sub i/, Y/sub i/) with F (X/sub i/, Y/sub i/)=0 and natural numbers n/sub i/, and a finite set of points Q/sub i/=(X/sub j/, Y/sub j/) with F(X/sub j/, Y/sub j/)=0 and natural numbers m/sub j/. The problem is to decide whether there is a rational function which has zeros at each point P/sub i/ of order n/sub i/, poles at each Q/sub j/ of order m/sub j/, and no zeros or poles anywhere else on C. One would also like to construct such a rational function if one exists. An efficient algorithm for solving this problem when the given plane curve has only ordinary multiple points is given.<>
研究了在给定曲线上构造有理函数和相交曲线的几个计算问题。第一个问题是在给定曲线上构造一个具有规定零点和极点的有理函数。更准确地说，设C为光滑投影曲线，并假设给定一个仿射平面模型F(x,y)=0，对C有一个有限点集P/sub i/=(x /sub i/， y /sub i/)， F(x /sub i/， y /sub i/)=0，自然数n/sub i/，和一个有限点集Q/sub i/=(x /sub j/， y /sub j/)， F(x /sub j/， y /sub j/)=0，自然数m/sub j/。问题是确定是否存在一个有理函数，它在每个点P/ i/ (n/ i/)处为零，在每个点Q/ j/ (m/ j/)处为极，而在c上其他地方没有零或极，如果存在的话，我们也想构造这样一个有理函数。给出了当给定平面曲线只有普通多点时求解该问题的一种有效算法。
{"title":"Efficient algorithms for the Riemann-Roch problem and for addition in the Jacobian of a curve","authors":"Ming-Deh A. Huang, D. Ierardi","doi":"10.1109/SFCS.1991.185435","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185435","url":null,"abstract":"Several computational problems concerning the construction of rational functions and intersecting curves over a given curve are studied. The first problem is to construct a rational function with prescribed zeros and poles over a given curve. More precisely, let C be a smooth projective curve and assume as given an affine plane model F(x,y)=0 for C, a finite set of points P/sub i/=(X/sub i/, Y/sub i/) with F (X/sub i/, Y/sub i/)=0 and natural numbers n/sub i/, and a finite set of points Q/sub i/=(X/sub j/, Y/sub j/) with F(X/sub j/, Y/sub j/)=0 and natural numbers m/sub j/. The problem is to decide whether there is a rational function which has zeros at each point P/sub i/ of order n/sub i/, poles at each Q/sub j/ of order m/sub j/, and no zeros or poles anywhere else on C. One would also like to construct such a rational function if one exists. An efficient algorithm for solving this problem when the given plane curve has only ordinary multiple points is given.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125275690","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185406
F. Leighton, Yuan Ma, C. Plaxton
The problem of constructing a sorting circuit that will work well even if a constant fraction of its comparators fail at random is addressed. Two types of comparator failure are considered: passive failures, which result in no comparison being made (i.e., the items being compared are output in the same order that they are input), and destructive failures, which result in the items being output in the reverse of the correct order. In either scenario, it is assumed that each comparator is faulty with some constant probability rho , and a circuit is said to be fault-tolerant if it performs some desired function with high probability given that each comparator fails with probability rho . One passive and two destructive circuits are constructed.<>
{"title":"Highly fault-tolerant sorting circuits","authors":"F. Leighton, Yuan Ma, C. Plaxton","doi":"10.1109/SFCS.1991.185406","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185406","url":null,"abstract":"The problem of constructing a sorting circuit that will work well even if a constant fraction of its comparators fail at random is addressed. Two types of comparator failure are considered: passive failures, which result in no comparison being made (i.e., the items being compared are output in the same order that they are input), and destructive failures, which result in the items being output in the reverse of the correct order. In either scenario, it is assumed that each comparator is faulty with some constant probability rho , and a circuit is said to be fault-tolerant if it performs some desired function with high probability given that each comparator fails with probability rho . One passive and two destructive circuits are constructed.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122563189","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185346
Frank Hoffmann, M. Kaufmann, K. Kriegel
Art gallery problems which have been extensively studied over the last decade ask how to station a small (minimum) set of guards in a polygon such that every point of the polygon is watched by at least one guard. The graph-theoretic formulation and solution to the gallery problem for polygons in standard form is given. A complexity analysis is carried out, and open problems are discussed.<>
{"title":"The art gallery theorem for polygons with holes","authors":"Frank Hoffmann, M. Kaufmann, K. Kriegel","doi":"10.1109/SFCS.1991.185346","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185346","url":null,"abstract":"Art gallery problems which have been extensively studied over the last decade ask how to station a small (minimum) set of guards in a polygon such that every point of the polygon is watched by at least one guard. The graph-theoretic formulation and solution to the gallery problem for polygons in standard form is given. A complexity analysis is carried out, and open problems are discussed.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"120 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117297741","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185430
A. Andersson, T. Ottmann
The authors present a solution to the dictionary problem where each subset of size n of an ordered universe is represented by a unique structure, containing a (unique) binary search tree. The structure permits the execution of search, insert, and delete operations in O(n/sup 1/3/) time in the worst case. They also give a general lower bound, stating that for any unique representation of a set in a graph of, bounded outdegree, one of the operations search or update must require a cost of Omega (n/sup 1/3/) Therefore, the result sheds new light on previously claimed lower bounds for unique binary search tree representations.<>
{"title":"Faster uniquely represented dictionaries","authors":"A. Andersson, T. Ottmann","doi":"10.1109/SFCS.1991.185430","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185430","url":null,"abstract":"The authors present a solution to the dictionary problem where each subset of size n of an ordered universe is represented by a unique structure, containing a (unique) binary search tree. The structure permits the execution of search, insert, and delete operations in O(n/sup 1/3/) time in the worst case. They also give a general lower bound, stating that for any unique representation of a set in a graph of, bounded outdegree, one of the operations search or update must require a cost of Omega (n/sup 1/3/) Therefore, the result sheds new light on previously claimed lower bounds for unique binary search tree representations.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130106462","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}
Jeerey Scott, Vitter P Krishnan, Jeerey Scott Vitter, P. Krishnan
A form of the competitive philosophy is applied to the problem of prefetching to develop an optimal universal prefetcher in terms of fault ratio, with particular applications to large-scale databases and hypertext systems. The algorithms are novel in that they are based on data compression techniques that are both theoretically optimal and good in practice. Intuitively, in order to compress data effectively, one has to be able to predict feature data well, and thus good data compressors should be able to predict well for purposes of prefetching. It is shown for powerful models such as Markov sources and mth order Markov sources that the page fault rates incurred by the prefetching algorithms presented are optimal in the limit for almost all sequences of page accesses.<>
{"title":"Optimal prefetching via data compression","authors":"Jeerey Scott, Vitter P Krishnan, Jeerey Scott Vitter, P. Krishnan","doi":"10.1145/234752.234753","DOIUrl":"https://doi.org/10.1145/234752.234753","url":null,"abstract":"A form of the competitive philosophy is applied to the problem of prefetching to develop an optimal universal prefetcher in terms of fault ratio, with particular applications to large-scale databases and hypertext systems. The algorithms are novel in that they are based on data compression techniques that are both theoretically optimal and good in practice. Intuitively, in order to compress data effectively, one has to be able to predict feature data well, and thus good data compressors should be able to predict well for purposes of prefetching. It is shown for powerful models such as Markov sources and mth order Markov sources that the page fault rates incurred by the prefetching algorithms presented are optimal in the limit for almost all sequences of page accesses.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"9 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121207230","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185443
H. Saran, V. Vazirani
Two simple approximation algorithms are presented for the minimum k-cut problem. Each algorithm finds a k-cut having weight within a factor of (2-2/k) of the optimal. One of the algorithms is particularly efficient, requiring a total of only n-1 maximum flow computations for finding a set of near-optimal k-cuts, one for each value of k between 2 and n.<>
{"title":"Finding k-cuts within twice the optimal","authors":"H. Saran, V. Vazirani","doi":"10.1109/SFCS.1991.185443","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185443","url":null,"abstract":"Two simple approximation algorithms are presented for the minimum k-cut problem. Each algorithm finds a k-cut having weight within a factor of (2-2/k) of the optimal. One of the algorithms is particularly efficient, requiring a total of only n-1 maximum flow computations for finding a set of near-optimal k-cuts, one for each value of k between 2 and n.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128971559","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}
Pub Date : 1991-09-01DOI: 10.1109/SFCS.1991.185414
M. Naor, R. Roth
Given a distributed network of processors represented by an undirected graph G=(V, E) and a file size k, the problem of distributing an arbitrary file w of k bits among all nodes of the network G is considered. Memory devices are to be assigned to the node of G such that, by accessing the memory of its own and of its adjacent nodes, each node can reconstruct the contents of w. The objective is to minimize the total size memory in the network. A file distribution scheme that realizes this objective for k>>log Delta /sub G/, where Delta /sub G/, stands for the maximum degree in G, is presented. For this range of k, the total size of memory required by the suggested scheme approaches an integer programming lower bound on that size.<>
{"title":"Optimal file sharing in distributed networks","authors":"M. Naor, R. Roth","doi":"10.1109/SFCS.1991.185414","DOIUrl":"https://doi.org/10.1109/SFCS.1991.185414","url":null,"abstract":"Given a distributed network of processors represented by an undirected graph G=(V, E) and a file size k, the problem of distributing an arbitrary file w of k bits among all nodes of the network G is considered. Memory devices are to be assigned to the node of G such that, by accessing the memory of its own and of its adjacent nodes, each node can reconstruct the contents of w. The objective is to minimize the total size memory in the network. A file distribution scheme that realizes this objective for k>>log Delta /sub G/, where Delta /sub G/, stands for the maximum degree in G, is presented. For this range of k, the total size of memory required by the suggested scheme approaches an integer programming lower bound on that size.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"88 31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130784841","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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