Related papers: Polynomially Correlated Knapsack is NP-complete
A valid inequality \alpha^Tx \ge \alpha_0 for a set covering problem is said to have pitch <= k ( a positive integer) if the k smallest positive \alpha_j sum to at least alpha_0. This paper presents a new, simple derivation of a relaxation…
We develop a novel mathematical programming approximation framework to tackle the stochastic knapsack problem. In this problem, the decision maker considers items for which either weights or values, or both, are random. The aim is to select…
Given two $k$-graphs $H$ and $F$, a perfect $F$-packing in $H$ is a collection of vertex-disjoint copies of $F$ in $H$ which together cover all the vertices in $H$. In the case when $F$ is a single edge, a perfect $F$-packing is simply a…
In this paper, we obtain a number of new simple pseudo-polynomial time algorithms on the well-known knapsack problem, focusing on the running time dependency on the number of items $n$, the maximum item weight $w_\mathrm{max}$, and the…
We investigate the complexity of a puzzle that turns out to be NL-complete.
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing (collapsing) a face of dimension at most d-1 that is contained in a unique maximal face. We prove that the algorithmic question whether a…
The Set-union Knapsack Problem (SUKP) is a generalization of the popular 0-1 knapsack problem. Given a set of weighted elements and a set of items with profits where each item is composed of a subset of elements, the SUKP involves packing a…
Sumsets are central objects in additive combinatorics. In 2007, Granville asked whether one can efficiently recognize whether a given set $S$ is a sumset, i.e. whether there is a set $A$ such that $A+A=S$. Granville suggested an algorithm…
NP-Complete problems have an important attribute that if one NP-Complete problem can be solved in polynomial time, all NP-Complete problems will have a polynomial solution. The 3-CNF-SAT problem is a NP-Complete problem and the primary…
The Knapsack Problem (KP) and its generalization, the Bounded Knapsack Problem (BKP), are classical NP-hard problems with numerous practical applications, and despite being introduced over 25 years ago, the solvers COMBO and BOUKNAP remain…
In this paper we show that the Mastermind Satisfiability Problem (MSP) is NP-complete. The Mastermind is a popular game which can be turned into a logical puzzle called Mastermind Satisfiability Problem in a similar spirit to the…
We prove that completing an untimed, unbounded track in TrackMania Nations Forever is NP-complete by using a reduction from 3-SAT and showing that a solution can be checked in polynomial time.
This paper presents a novel and straight formulation, and gives a complete insight towards the understanding of the complexity of the problems of the so called NP-Class. In particular, this paper focuses in the Searching of the Optimal…
In this letter, we formulate a generalized decision fusion problem (GDFP) for sensing with centralized hard decision fusion. We show that various new and existing decision fusion rules are special cases of the proposed GDFP. We then relate…
In this paper, we study the following knapsack problem: Given a list of squares with profits, we are requested to pack a sublist of them into a rectangular bin (not a unit square bin) to make profits in the bin as large as possible. We…
We determine the exact threshold of satisfiability for random instances of a particular NP-complete constraint satisfaction problem (CSP). This is the first random CSP model for which we have determined a precise linear satisfiability…
A polynomial algorithm is obtained for the NP-complete linear ordering problem.
In graph realization problems one is given a degree sequence and the task is to decide whether there is a graph whose vertex degrees match to the given sequence. This realization problem is known to be polynomial-time solvable when the…
A Boolean constraint satisfaction instance is a conjunction of constraint applications, where the allowed constraints are drawn from a fixed set B of Boolean functions. We consider the problem of determining whether two given constraint…