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On-line algorithms for polynomially solvable satisfiability problems

Giorgio Ausiello, Giuseppe F. Italiano
1991 The Journal of Logic Programming  
D Given a propositional Horn formula, we show how to maintain on-line information about its satisfiability during the insertion of new clauses.  ...  The on-line time and space complexity of these operations is also analyzed. a  ...  We would like to thank the referees for their helpful comments and valuable suggestions, which improved the presentation of the paper.  ... 
doi:10.1016/0743-1066(91)90006-b fatcat:tnir2qnbt5bk3pciui3vdln2cy

Linear Network Codes and Systems of Polynomial Equations

Randall Dougherty, Chris Freiling, Kenneth Zeger
2008 IEEE Transactions on Information Theory  
(Hence, the problems of network scalar-linear solvability and polynomial collection solvability have the same complexity.)  ...  We say that a network and a polynomial collection are solvably equivalent if for each field F the network has a scalar-linear solution over F if and only if the polynomial collection is solvable over F  ...  ACKNOWLEDGMENT The authors wish to thank Sidharth Jaggi and Søren Riis for a helpful discussion.  ... 
doi:10.1109/tit.2008.920209 fatcat:mkekcia6sfa7faacw4x7zyhrji

Linear network codes and systems of polynomial equations

Randall Dougherty, Chris Freiling, Kenneth Zeger
2008 2008 IEEE International Symposium on Information Theory  
(Hence, the problems of network scalar-linear solvability and polynomial collection solvability have the same complexity.)  ...  We say that a network and a polynomial collection are solvably equivalent if for each field F the network has a scalar-linear solution over F if and only if the polynomial collection is solvable over F  ...  ACKNOWLEDGMENT The authors wish to thank Sidharth Jaggi and Søren Riis for a helpful discussion.  ... 
doi:10.1109/isit.2008.4595306 dblp:conf/isit/DoughertyFZ08 fatcat:xncknnvgx5aerf4xflxyhoo7li

Generating all maximal induced subgraphs for hereditary and connected-hereditary graph properties

Sara Cohen, Benny Kimelfeld, Yehoshua Sagiv
2008 Journal of computer and system sciences (Print)  
These algorithms imply that when attempting to efficiently solve the maximal P-subgraphs problem for a specific P, it is sufficient to solve the restricted case.  ...  Formally, given a graph G, the maximal P-subgraphs problem is to generate all maximal induced subgraphs of G that satisfy P.  ...  Acknowledgments The authors thank the anonymous referees for helpful suggestions and for pointing out important related work. Appendix A. Auxiliary procedures A.1. ExtendMax  ... 
doi:10.1016/j.jcss.2008.04.003 fatcat:b4t2bwzupfaf7npwgjhbjfsuym

A recursive method for solving unconstrained tangential interpolation problems

T. Boros, A.H. Sayed, T. Kailath
1999 IEEE Transactions on Automatic Control  
The algorithm also provides coprime factorizations for all rational interpolants and can be used to solve polynomial interpolation problems such as the general Hermite matrix interpolation problem.  ...  An efficient recursive solution is presented for the one-sided unconstrained tangential interpolation problem.  ...  Kamali, and the reviewers of the manuscript for helpful remarks and references.  ... 
doi:10.1109/9.751341 fatcat:ufjlettv6zb4bkdzsdjcxgdybq

Non deterministic polynomial optimization problems and their approximations

A. Paz, S. Moran
1981 Theoretical Computer Science  
This prompted many researchers CO develop and study polynomial approximation schemes for NP-problems.  ...  A unified and general framework for the study of nondeterministic polynomial optimization problems (NPDP) is presented and some prop,erties of NPOP's are investigated.  ...  Remark A,& The time required for the above reduction differs from that of Cook's original reduction by at most 0( f(Z(a))*) steps required 60 define the weight function W.  ... 
doi:10.1016/0304-3975(81)90081-5 fatcat:cqzybi4pxzdcto2yiogaqgj6ba

Complexity of a Disjoint Matching Problem on Bipartite Graphs [article]

Gregory J. Puleo
2015 arXiv   pre-print
When |S|≥ |X|-1, this question is solvable by finding an appropriate factor of the graph. In contrast, we show that when S is allowed to be an arbitrary subset of X, the problem is NP-hard.  ...  For any fixed k, the problem SDM is polynomial-time solvable on instances with |S| ≤ k: we can iterate over the O(|Y | k ) possible choices for M 2 , and for each possible choice, check whether G − M 2  ...  For fixed k > 1, is there a polynomial-time algorithm to solve SDM on instances with |S| ≥ |X| − k? Hence Hall's Condition holds for H.  ... 
arXiv:1506.06157v1 fatcat:3isxlmzlvffwxbb4mxge5c3lfi

Hiding Solutions in Random Satisfiability Problems: A Statistical Mechanics Approach

W. Barthel, A. K. Hartmann, M. Leone, F. Ricci-Tersenghi, M. Weigt, R. Zecchina
2002 Physical Review Letters  
On the basis of statistical mechanics results, we propose random generators of hard and satisfiable instances for the 3-satisfiability problem (3SAT).  ...  A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal  ...  It is based on a NP (nondeterministic polynomial time)-complete problem [1] , namely, 3-satisfiability (3-SAT).  ... 
doi:10.1103/physrevlett.88.188701 pmid:12005728 fatcat:lbqrp62sgjhlrjf5bhnamgzgyi

Solvability by radicals is in polynomial time

Susan Landau, Gary Lee Miller
1985 Journal of computer and system sciences (Print)  
Lagrange published a treatise which discussed why the methods that worked for polynomials of degree less than five did not extend to quintic polynomials [S], hoping to shed some light on the problem.  ...  A polynomial time algorithm is presented for the founding question of Galois theory: determining solvability by radicals of a manic irreducible polynomial over the integers.  ...  If a group is returned, we call one of the standard algorithms for testing solvability of a group [17, 6) .  ... 
doi:10.1016/0022-0000(85)90013-3 fatcat:acjvol7675brdgh6tsluvtkjeq

Generating All Maximal Induced Subgraphs for Hereditary, Connected-Hereditary and Rooted-Hereditary Properties [article]

Sara Cohen, Yehoshua Sagiv
2004 arXiv   pre-print
The maximal P-subgraphs problem is reduced to restricted versions of this problem by providing algorithms that solve the general problem, assuming that an algorithm for a restricted version is given.  ...  The complexity of the algorithms are analyzed in terms of total polynomial time, incremental polynomial time and the complexity class P-enumerable.  ...  Similarly, every problem that is solvable in incremental polynomial time is also solvable in total polynomial time.  ... 
arXiv:cs/0410039v1 fatcat:xutjxuyoo5cb7i66lkthqz5dnm

Polynomial Time Inductive Inference of Cograph Pattern Languages from Positive Data [chapter]

Yuta Yoshimura, Takayoshi Shoudai, Yusuke Suzuki, Tomoyuki Uchida, Tetsuhiro Miyahara
2012 Lecture Notes in Computer Science  
Toward effective data mining for graph structured data, we introduce a graph pattern expression, called a cograph pattern, based on cographs.  ...  We show that the class of cograph pattern languages is polynomial time inductively inferable from positive data.  ...  We propose an algorithm Matching-CT P to solve the membership problem for cotree patterns in polynomial time, based on a polynomial time pattern matching algorithm for linear interval graph patterns [  ... 
doi:10.1007/978-3-642-31951-8_32 fatcat:lbjn5mimszhydhtm5joanvtx6q

An optimization approach for the satisfiability problem

S. Noureddine
2015 Applied Computing and Informatics  
We describe a new approach for solving the satisfiability problem by geometric programming. We focus on the theoretical background and give details of the algorithmic procedure.  ...  The algorithm is provably efficient as geometric programming is in essence a polynomial problem. The correctness of the algorithm is discussed.  ...  x * is solvable in polynomial time.  ... 
doi:10.1016/j.aci.2011.11.002 fatcat:5b7m6gzqerdfbaanty3ezwm73m

Detecting strong cliques [article]

Ademir Hujdurović, Martin Milanič, Bernard Ries
2018 arXiv   pre-print
We study the computational complexity of six algorithmic decision problems related to strong cliques in graphs and almost completely determine their complexity in the classes of chordal graphs, weakly  ...  chordal graphs, line graphs and their complements, and graphs of maximum degree at most three.  ...  Acknowledgements The authors are grateful to Mark Ellingham for providing them with a copy of Ramey's PhD thesis [37] and of paper [12] .  ... 
arXiv:1808.08817v1 fatcat:lignkmdlyverlcit4wfkquti7e

An algebraic approach to network coding

R. Koetter, M. Medard
2003 IEEE/ACM Transactions on Networking  
We also consider the problem of network recovery for nonergodic link failures.  ...  Building on recent work by Li et al., who examined the network capacity of multicast networks, we extend the network coding framework to arbitrary networks and robust networking.  ...  The network problem is solvable if and only if the Min-Cut Max-Flow bound is satisfied for all connections in .  ... 
doi:10.1109/tnet.2003.818197 fatcat:cpf6ybzugveuzd7bqobauvhyve

A Performance Study of Energy Minimization for Interleaved and Localized FDMA [article]

Lei You, Lei Lei, Di Yuan
2017 arXiv   pre-print
When the user demand can be satisfied in both LFDMA and IFDMA, LFDMA performs slightly better than IFDMA. However Min- Power is polynomial-time solvable for IFDMA whereas it is not for LFDMA.  ...  In this paper, we prove that Min-Power is polynomial-time solvable for interleaved SC-FDMA (IFDMA).  ...  . • We show that the Min-Power for IFDMA is polynomialtime solvable. • A polynomial-time algorithm MPCA is developed to solve the Min-Power problem in IFDMA. • Numerically, we find that on Min-Power, LFDMA  ... 
arXiv:1602.08469v2 fatcat:zggcx7corbgrbabcnw26zrk7tm
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