Filters








92,461 Hits in 5.9 sec

Faster Space-Efficient Algorithms for Subset Sum, k-Sum and Related Problems [article]

Nikhil Bansal, Shashwat Garg, Jesper Nederlof, Nikhil Vyas
2017 arXiv   pre-print
We present space efficient Monte Carlo algorithms that solve Subset Sum and Knapsack instances with n items using O^*(2^0.86n) time and polynomial space, where the O^*(·) notation suppresses factors polynomial  ...  We also show that for any constant k≥ 2, random instances of k-Sum can be solved using O(n^k-0.5polylog(n)) time and O( n) space, without the assumption of random access to random bits.  ...  Introduction The Subset Sum problem and the closely related Knapsack problem are two of the most basic NP-Complete problems.  ... 
arXiv:1612.02788v2 fatcat:ea2ymdqbnfay3enmx32cxfa5ui

Faster Space-Efficient Algorithms for Subset Sum, $k$-Sum, and Related Problems

Nikhil Bansal, Shashwat Garg, Jesper Nederlof, Nikhil Vyas
2018 SIAM journal on computing (Print)  
We also show that for any constant k ≥ 2, random instances of k-Sum can be solved using O(n k−0.5 polylog(n)) time and O(log n) space, without the assumption of random access to random bits.  ...  We present randomized algorithms that solve Subset Sum and Knapsack instances with n items in O * (2 0.86n ) time, where the O * (·) notation suppresses factors polynomial in the input size, and polynomial  ...  Introduction The Subset Sum problem and the closely related Knapsack problem are two of the most basic NP-Complete problems.  ... 
doi:10.1137/17m1158203 fatcat:3qkxhuryorccboktcsuxh5lxsa

Optimal Sequential Multi-Way Number Partitioning

Richard E. Korf, Ethan L. Schreiber, Michael D. Moffitt
2014 International Symposium on Artificial Intelligence and Mathematics  
Given a multiset of n positive integers, the NP-complete problem of number partitioning is to assign each integer to one of k subsets, such that the largest sum of the integers assigned to any subset is  ...  Number partitioning is closely related to bin-packing, and advances in either problem can be applied to the other.  ...  Horowitz and Sahni (HS) Horowitz and Sahni (HS) presented a faster algorithm for the subset sum problem. It divides the n integers into two "half" sets a and c, each of size n/2.  ... 
dblp:conf/isaim/KorfSM14 fatcat:fwgstyqztzdmldm3o7ohs42gqq

Counting Paths and Packings in Halves [article]

Andreas Björklund and Thore Husfeldt and Petteri Kaski and Mikko Koivisto
2009 arXiv   pre-print
space, the bounds hold if multiplied by 3^k/2 or 5^mk/2, respectively.  ...  their subsets.  ...  This research was supported in part by the Academy of Finland, Grants 117499 (P.K.) and 125637 (M.K.).  ... 
arXiv:0904.3093v1 fatcat:asuyur4l45d2tpsekdyx5cp2yy

Equal-Subset-Sum Faster Than the Meet-in-the-Middle

Marcin Mucha, Jesper Nederlof, Jakub Pawlewicz, Karol Wegrzycki, Michael Wagner
2019 European Symposium on Algorithms  
Additionally, we analyse the polynomial space algorithm for Equal-Subset-Sum. A naive polynomial space algorithm for Equal-Subset-Sum runs in O * (3 n ) time.  ...  In the Equal-Subset-Sum problem, we are given a set S of n integers and the problem is to decide if there exist two disjoint nonempty subsets A, B ⊆ S, whose elements sum up to the same value.  ...  Acknowledgements The authors would like to thank anonymous reviewers for their remarks and suggestions.  ... 
doi:10.4230/lipics.esa.2019.73 dblp:conf/esa/MuchaNPW19 fatcat:lmbwjpjidrfi5kdqj2bi4sazhq

Space-Efficient Las Vegas Algorithms for K-SUM [article]

Joshua Wang
2013 arXiv   pre-print
Using hashing techniques, this paper develops a family of space-efficient Las Vegas randomized algorithms for k-SUM problems.  ...  It also establishes a new time-space upper bound for SUBSET-SUM, which can be solved by a Las Vegas algorithm in O^*(2^(1-√(/9β))n) time and O^*(2^β n) space, for any β∈ [0, /32].  ...  Acknowledgements I would like to thank Ryan Williams for providing helpful pointers to existing literature, insightful discussions, and proofreading.  ... 
arXiv:1303.1016v2 fatcat:m4qzeqv62zbkljc4g43clz4aqu

Cached Iterative Weakening for Optimal Multi-Way Number Partitioning

Ethan Schreiber, Richard Korf
2014 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
The NP-hard number-partitioning problem is to separate a multiset S of n positive integers into k subsets, such that the largest sum of the integers assigned to any subset is minimized.  ...  The previous state of the art is represented by three different algorithms depending on the values of n and k. We provide one algorithm which outperforms all previous algorithms for k >= 4.  ...  Number partitioning is closely related to the bin-packing problem (Garey and Johnson 1979) .  ... 
doi:10.1609/aaai.v28i1.9122 fatcat:34qwpmrskbenrjzijzuxn2d52m

Faster and Space Efficient Exact Exponential Algorithms: Combinatorial and Algebraic Approaches [chapter]

Dongxiao Yu, Yuexuan Wang, Qiang-Sheng Hua, Francis C.M. Lau
2013 Handbook of Combinatorial Optimization  
For illustration, exact algorithms arising from the use of these techniques for some optimization and counting problems are given. ⋆ Corresponding author (fcmlau@cs.hku.hk).  ...  The discussed techniques can be used either to derive faster exact exponential algorithms, or to significantly reduce the space requirements while without increasing the running time.  ...  Faster polynomial space exact algorithms for subset sum were also proposed in the same paper, and by combining with subset convolution, they gave polynomial space exact algorithms for the Steiner tree  ... 
doi:10.1007/978-1-4419-7997-1_38 fatcat:bn4ey6gtzndabnok4onyncorzy

Deterministic Time-Space Tradeoffs for k-SUM [article]

Andrea Lincoln, Virginia Vassilevska Williams, Joshua R. Wang, R. Ryan Williams
2016 arXiv   pre-print
Given a set of numbers, the $k$-SUM problem asks for a subset of $k$ numbers that sums to zero.  ...  We present a time and space efficient deterministic self-reduction for the $k$-SUM problem which holds for both models, and has many interesting consequences.  ...  Baran, Demaine, and Patrascu use hashing to get subquadratic algorithms for 3-SUM [7] ; Patrascu uses it to reduce 3-SUM to Convolution 3-SUM [20] ; Wang uses it to produce a family of linear-space algorithms  ... 
arXiv:1605.07285v1 fatcat:lqax3ksdsjcvrpuhngobdtn2yy

Equal-Subset-Sum Faster Than the Meet-in-the-Middle [article]

Marcin Mucha, Jesper Nederlof, Jakub Pawlewicz, Karol Węgrzycki
2019 arXiv   pre-print
Additionally, we analyse the polynomial space algorithm for Equal-Subset-Sum. A naive polynomial space algorithm for Equal-Subset-Sum runs in O^*(3^n) time.  ...  In the Equal-Subset-Sum problem, we are given a set S of n integers and the problem is to decide if there exist two disjoint nonempty subsets A,B ⊆ S, whose elements sum up to the same value.  ...  In Appendix B we show that a faster algorithm than O * (1.1893 n ) for Equal-Subset-Sum would yield a faster than O * (2 n/2 ) algorithm for Subset-Sum.  ... 
arXiv:1905.02424v2 fatcat:a6jusw7n4vefjletqljx3lnxhy

A complete anytime algorithm for number partitioning

Richard E. Korf
1998 Artificial Intelligence  
Given a set of numbers, the two-way number partitioning problem is to divide them into two subsets, so that the sum of the numbers in each subset are as nearly equal as possible.  ...  outperforms the best previously-known algorithms for large problem instances.  ...  Thanks to Wheeler, Ken Boese, Alex Fukunaga and Andrew Kahng for helpful discussions concerning this research, and to Pierre Hasenfratz for comments on an earlier draft.  ... 
doi:10.1016/s0004-3702(98)00086-1 fatcat:5bvt6n76nbf57mektzyo4cltfa

An O*(2^n ) Algorithm for Graph Coloring and Other Partitioning Problems via Inclusion--Exclusion

Mikko Koivisto
2006 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)  
Our algorithms do not rely on any intrinsic properties of the functions f c . Thus, for specific problems, such as the chromatic number problem, even faster algorithms may exist.  ...  This problem subsumes various classical graph partitioning problems, such as graph coloring, domatic partitioning, and MAX k-CUT, as well as machine learning problems like decision graph learning and model-based  ...  Acknowledgements I am grateful to Heikki Mannila for valuable conversations on this work.  ... 
doi:10.1109/focs.2006.11 dblp:conf/focs/Koivisto06 fatcat:rjb5ch4azbew5brgekdihsg224

Optimal measurements for the dihedral hidden subgroup problem [article]

Dave Bacon, Andrew M. Childs, Wim van Dam
2005 arXiv   pre-print
In particular, we show that an efficient quantum algorithm for a restricted version of the optimal measurement would imply an efficient quantum algorithm for the subset sum problem, and conversely, that  ...  Finally, we consider implementing the optimal measurement by a quantum circuit, and thereby establish further connections between the dihedral hidden subgroup problem and average case subset sum problems  ...  We thank Carlos Mochon and Frank Verstraete for helpful discussions of Theorem 1, and Abie Flaxman for correspondence regarding the algorithm in [16] and an earlier version thereof.  ... 
arXiv:quant-ph/0501044v1 fatcat:cgvue7uxerbmnltvowgadqxv6u

Exact Parameterized Multilinear Monomial Counting via k-Layer Subset Convolution and k-Disjoint Sum [chapter]

Dongxiao Yu, Yuexuan Wang, Qiang-Sheng Hua, Francis C. M. Lau
2011 Lecture Notes in Computer Science  
We also present a polynomial space algorithm with time bound O * (2 k n k ).  ...  By reducing the #k-path problem and the #m-set kpacking problem to the exact multilinear k-monomial counting problem, we give algorithms for these two problems that match the fastest known results presented  ...  For more details, please refer to [3] . Faster Algorithms for Exact Multilinear k-Monomial Counting k-Disjoint Sum Definition 3.  ... 
doi:10.1007/978-3-642-22685-4_7 fatcat:uhc6nncgsfci7ag5hxnntwjoxy

Fast Low-Space Algorithms for Subset Sum [article]

Ce Jin, Nikhil Vyas, Ryan Williams
2020 arXiv   pre-print
For parameter 1≤ k≤min{n,t}, we present a randomized algorithm running in Õ((n+t)· k) time and O((t/k) polylog (nt)) space.  ...  In this paper we present algorithms for Subset Sum with Õ(nt) running time and much lower space requirements than Bellman's algorithm, as well as that of prior work.  ...  Acknowledgements Ce Jin would like to thank Jun Su and Ruixiang Zhang for pointing him to the Bombieri-Vinogradov theorem.  ... 
arXiv:2011.03819v1 fatcat:iyllwlncfbgyheiubao5pxt5im
« Previous Showing results 1 — 15 out of 92,461 results