A Linear Solution of Subset Sum Problem by Using Membrane Creation

2005 ◽  
pp. 258-267 ◽  
Author(s):  
M. A. Gutiérrez-Naranjo ◽  
M. J. Pérez-Jiménez ◽  
F. J. Romero-Campero
Keyword(s):  
Linear Solution ◽  
Subset Sum Problem ◽  
Subset Sum

scholarly journals Minimum constraint removal problem for line segments is NP-hard

2022 ◽  
Author(s):  
Bahram Sadeghi Bigham
Keyword(s):  
Free Path ◽  
Np Hard ◽  
Convex Polygons ◽  
Linear Solution ◽  
Line Segments ◽  
Subset Sum Problem ◽  
Starting Point ◽  
Subset Sum ◽  
Feasible Path ◽  
Minimum Constraints

In the minimum constraint removal ([Formula: see text]), there is no feasible path to move from a starting point towards the goal, and the minimum constraints should be removed in order to find a collision-free path. It has been proved that [Formula: see text] problem is NP-hard when constraints have arbitrary shapes or even they are in shape of convex polygons. However, it has a simple linear solution when constraints are lines and the problem is open for other cases yet. In this paper, using a reduction from Subset Sum problem, in three steps, we show that the problem is NP-hard for both weighted and unweighted line segments.

An Algorithm Using Modular Arithmetic for the Subset Sum Problem

1990 ◽  
Vol 21 (2) ◽  
pp. 1-10
Author(s):  
Toshiro Tachibana ◽  
Hideo Nakano ◽  
Yoshiro Nakanishi ◽  
Mitsuru Nakao
Keyword(s):  
Modular Arithmetic ◽  
Subset Sum Problem ◽  
Subset Sum

scholarly journals Trivial geometric heuristic for subset sum problem

2017 ◽  
Author(s):  
R U
Keyword(s):  
Greedy Algorithm ◽  
Dimensional Space ◽  
Approximate Solutions ◽  
Exact Algorithms ◽  
Approximation Schemes ◽  
Brute Force ◽  
Discrete Structure ◽  
Subset Sum Problem ◽  
Subset Sum ◽  
Hyper Plane

All exact algorithms for solving subset sum problem (SUBSET\_SUM) are exponential (brute force, branch and bound search, dynamic programming which is pseudo-polynomial). To find the approximate solutions both a classical greedy algorithm and its improved variety, and different approximation schemes are used.This paper is an attempt to build another greedy algorithm by transferring representation of analytic geometry to such an object of discrete structure as a set. Set of size $n$ is identified with $n$-dimensional space with Euclidean metric, the subset-sum is identified with (hyper)plane.

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