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Dense Subset Sum may be the hardest [article]

Per Austrin, Mikko Koivisto, Petteri Kaski, Jesper Nederlof
2015 arXiv   pre-print
The Subset Sum problem asks whether a given set of n positive integers contains a subset of elements that sum up to a given target t.  ...  Continuing an earlier work [STACS 2015], we study Subset Sum parameterized by the maximum bin size β, defined as the largest number of subsets of the n input integers that yield the same sum.  ...  An optimist may interpret this as an indication that truly faster algorithms indeed exist, while a pessimist may conclude the remaining instances must be the (strictly) hardest instances.  ... 
arXiv:1508.06019v1 fatcat:tupcp43vyje5fc5hske2alzwre

Dense Subset Sum May Be the Hardest

Per Austrin, Petteri Kaski, Mikko Koivisto, Jesper Nederlof, Marc Herbstritt
2016 Symposium on Theoretical Aspects of Computer Science  
The Subset Sum problem asks whether a given set of n positive integers contains a subset of elements that sum up to a given target t.  ...  Continuing an earlier work [STACS 2015], we study Subset Sum parameterized by the maximum bin size β, defined as the largest number of subsets of the n input integers that yield the same sum.  ...  σ 2 ± o γ (1) , |z −1 (1)| n = 1 − σ 2 + (1 − τ )σ 2 ± o γ (1) , |z −1 (2)| n = (1 − τ )σ 2 ± o γ (1) , 13:12 Dense Subset Sum May Be the Hardest Further Discussion Our original ambition was to resolve  ... 
doi:10.4230/lipics.stacs.2016.13 dblp:conf/stacs/AustrinKKN16 fatcat:xhlvjyiftvhnxg22jzm2epzvoy

Dense Subset Sum May Be the Hardest

Per Austrin, Petteri Kaski, Mikko Koivisto, Jesper Nederlof
unpublished
The Subset Sum problem asks whether a given set of n positive integers contains a subset of elements that sum up to a given target t.  ...  Continuing an earlier work [STACS 2015], we study Subset Sum parameterized by the maximum bin size β, defined as the largest number of subsets of the n input integers that yield the same sum.  ...  An optimist may interpret this as an indication that truly faster algorithms indeed exist, while a pessimist may conclude the remaining instances must be the (strictly) hardest instances.  ... 
fatcat:f3fhjakjdfbt7fgdiuy4qwwspq

From Approximate to Optimal Solutions: Constructing Pruning and Propagation Rules

Ian P. Gent, Toby Walsh
1997 International Joint Conference on Artificial Intelligence  
We show that the pruning rule adds essentially a constant factor overhead to runtime, whilst reducing search significantly. On the hardest problems, runtime can be reduced by an order of magnitude.  ...  be effective on other NP-complete problems.  ...  Subset sum Given a set is there a subset whose weights have a target sum Subset sum is problem SP13 in [Garey and Johnson, 1979] .  ... 
dblp:conf/ijcai/GentW97 fatcat:nte4xt7ibzh4lkwwmyeb36zvtq

Sharp estimate on the supremum of a class of partial sums of small i.i.d. random variables [article]

Peter Major
2014 arXiv   pre-print
In a subsequent paper [2] we shall give a sharp bound for the supremum of normalized sums of i.i.d. random variables in a more general case.  ...  We take an L_1-dense class of functions F on a measurable space (X, X) together with a sequence of independent, identically distributed X-space valued random variables ξ_1,...  ...  . , x N } be a finite set of N elements, and let X be the σ-algebra consisting of all subsets of X.  ... 
arXiv:1407.1224v1 fatcat:palzma2dfnbmpjlklvm3ee5tk4

Non-injective knapsack public-key cryptosystems

Jukka A. Koskinen
2001 Theoretical Computer Science  
Decryption is fairly slow and may produce more than one decipherment, but all alternative decipherments can be found. Disambiguating protocols are needed to determine the correct decipherment.  ...  Two public-key 0-1 knapsack cryptosystems are proposed, that have so high a density and use so weak a modular multiplication as a trapdoor, that known attacks can be avoided.  ...  The initial knapsack B 0 is to be dense, injective and small enough for complete enumeration of its subset sums. Decipherment can thus be carried out by table lookup.  ... 
doi:10.1016/s0304-3975(99)00297-2 fatcat:obysbpyseve4dluzllwmrg6bpu

Vector lattice approach to the Riesz and Stone Representation theorems [article]

Eugene Bilokopytov
2021 arXiv   pre-print
Let h ∈ F (A) be such that f, −f ≤ h. Since Qg does not depend on the disjoint representation, we may assume that h has the same one as f , i.e. there is w = γ i a i , such that Qw = h.  ...  In this article we focus on the "hardest part", and in our proof most of the heavy lifting is done by the vector lattice theory.  ... 
arXiv:2104.01576v1 fatcat:4r3c6iobubesrhrxqehvi7m6eu

A Hybrid-Similarity Exemplar Model for Predicting Distinctiveness Effects in Perceptual Old-New Recognition

Robert M. Nosofsky, Safa R. Zaki
2003 Journal of Experimental Psychology. Learning, Memory and Cognition  
In this case, large old-item distinctive effects were observed, with the nature of the effects being modulated by the structure of the test lists.  ...  In this case, any beneficial effects of distinctiveness were absent or small, regardless of the structure of the test list used to assess recognition memory.  ...  One concern that might be raised is that the proportion of old versus new items varied across the three testing conditions (complete set, fixed subset, and correlated subset).  ... 
doi:10.1037/0278-7393.29.6.1194 pmid:14622055 fatcat:mg4xnhtgcvcdvhdmswkyydg5de

Sharp estimate on the supremum of a class of sums of small i.i.d. random variables

Péter Major
2016 Stochastic Processes and their Applications  
Because of the special form of the functionsf j if a set of functionsF ε,ν ⊂F is an ε-dense subset ofF in the L 1 (ν) norm, then it is also a ε-dense subset ofF in the L 1 (ν) norm.  ...  elements which is an ε-dense set in F with respect to the L 1 (ν) norm with a probability measure ν, and f j ∈ F, but these functions may be not contained in F ′ .  ... 
doi:10.1016/j.spa.2015.07.016 fatcat:jmpkodqdpbbk5pkuyi6iq54wum

Coarser connected topologies

William G Fleissner, Jack Porter, Judith Roitman
2004 Topology and its Applications  
In the previous sentence, the separation property collectionwise normal can be replaced by other separation properties-for example, Hausdorff, Urysohn, regular, metrizable.  ...  We present a nowhere locally compact Hausdorff space X with no coarser connected Hausdorff topology, yet X is dense in a connected Hausdorff space Y .  ...  Let ξ n be the order type of X n . We may assume that {ξ n : n ∈ ω} is cofinal in β. (Let {β n : n ∈ ω} be cofinal in β, and make β n a subset of X n .)  ... 
doi:10.1016/j.topol.2003.10.007 fatcat:dyzpy3iycjcrhhcv3fafat3vf4

Asymptotic variation of L functions of one-variable exponential sums [article]

Hui June Zhu
2005 arXiv   pre-print
We prove that there is a Zariski dense open subset U defined over Q in A^d such that for every geometric point f(x) in U(Qbar) we have lim_p-->oo NP(f mod P) = HP(A^d), where P is any prime ideal in the  ...  Let d>2 and let p be a prime coprime to d. Let Z_pbar be the ring of integers of Q_pbar. Suppose f(x) is a degree-d polynomial over Qbar and Z_pbar.  ...  Suppose there is such a Zariski dense open subset U defined over Q in A d .  ... 
arXiv:math/0206284v3 fatcat:4rbt4vjz4ve3rmmjw7ybfvxadu

Convolutional neural networks for structured omics: OmicsCNN and the OmicsConv layer [article]

Giuseppe Jurman and Valerio Maggio and Diego Fioravanti and Ylenia Giarratano and Isotta Landi and Margherita Francescatto and Claudio Agostinelli and Marco Chierici and Manlio De Domenico and Cesare Furlanello
2017 arXiv   pre-print
In particular, for metagenomics data, a metric can be derived from the patristic distance on the phylogenetic tree.  ...  ., they can be endowed with a metric structure, enabling to adopt a convolutional based deep learning framework, e.g., for prediction.  ...  As a consequence, the direct application of deep networks to microarray, genetic or other omics can be disappointing, as found by Ditzler and coauthors [6] that claimed that deep learning "may not be  ... 
arXiv:1710.05918v1 fatcat:lf2qhbkehzcfvmw2vkewoy4oli

Asymptotic variation of L functions of one-variable exponential sums

H. J. Zhu
2004 Journal für die Reine und Angewandte Mathematik  
We prove that there is a Zariski dense open subset U defined over Q in A d such that for every geometric point f (x) in U(Q) and p large enough (depending only on f ) one has NP(f mod P) = GNP(A d ; Fp  ...  Suppose f ∈ A d (Q ∩ Zp), let NP(f (x) mod P) denote the q-adic Newton polygon of the L function L(f (x) mod P; T ) of exponential sums of f mod P.  ...  Suppose there is such a Zariski dense open subset U defined over Q in A d .  ... 
doi:10.1515/crll.2004.051 fatcat:kcnbf36yaza7xhlp6akz7tsgiy

Parallel modularity computation for directed weighted graphs with overlapping communities
Параллельное вычисление модулярности для направленных взвешенных графов с пересекающимися сообществами

M. Drobyshevskiy, A. Korshunov, D. Turdakov
2016 Proceedings of the Institute for System Programming of RAS  
The paper presents new versions of modularity measure for directed weighted graphs with overlapping communities. We consider several approaches to computing modularity and try to extend them.  ...  The only problem here is that the biggest community may have size square much more than sum of size squares of the rest ones, i.e. the chunk which gets this community will be overloaded.  ...  To achieve this we used a greedy algorithm, which iterates over communities in descending order and assigns each of them to a subset that has the smallest sum of size squares.  ... 
doi:10.15514/ispras-2016-28(6)-11 fatcat:5mgab4ph4zbytoj6gap2yulupe

IMFD IMPRESEE at TRECVID 2019: Ad-Hoc Video Search and Video To Text

Rodrigo Hernández, Jesus Perez-Martin, Nicolás Bravo, Juan Manuel Barrios, Benjamin Bustos
2019 TREC Video Retrieval Evaluation  
Second, for the VTT Matching and Ranking Task, we develop another deep learning model based on Word2VisualVec++, extracting temporal information of the video by using Dense Trajectories [16] and a clustering  ...  We participated in the task Ad-hoc Video Search (AVS) and the subtasks Description Generation and Matching and Ranking of Video to Text (VTT) task.  ...  Acknowledgements The authors of this paper would like to thank NIST and all the coordinators of TRECVID for organizing this event.  ... 
dblp:conf/trecvid/HernandezPBBB19 fatcat:uc57auanvzagfd5rbjfue7vm7q
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