Related papers: Solving Billion-Scale Knapsack Problems
We introduce and study a discrete multi-period extension of the classical knapsack problem, dubbed generalized incremental knapsack. In this setting, we are given a set of $n$ items, each associated with a non-negative weight, and $T$ time…
We study two canonical online optimization problems under capacity/budget constraints: the fractional one-way trading problem (OTP) and the integral online knapsack problem (OKP) under an infinitesimal assumption. Under the competitive…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
We apply the replica analysis established by Gardner to the multi-constraint continuous knapsack problem,which is one of the linear programming problems and a most fundamental problem in the field of operations research (OR). For a large…
We analyze the competitive ratio and the advice complexity of the online unbounded knapsack problem. An instance is given as a sequence of n items with a size and a value each, and an algorithm has to decide how often to pack each item into…
Combinatorial problems are a common challenge in business, requiring finding optimal solutions under specified constraints. While significant progress has been made with variational approaches such as QAOA, most problems addressed are…
Constrained optimization underlies crucial societal problems (for instance, stock trading and bandwidth allocation), but is often computationally hard (complexity grows exponentially with problem size). The big-data era urgently demands…
We formulate the knapsack problem (KP) as a statistical physics system and compute the corresponding partition function as an integral in the complex plane. The introduced formalism allows us to derive three statistical-physics-based…
Multi-armed bandit problems are the predominant theoretical model of exploration-exploitation tradeoffs in learning, and they have countless applications ranging from medical trials, to communication networks, to Web search and advertising.…
We prove new lower bounds for suitable competitive ratio measures of two relaxed online packing problems: online removable multiple knapsack, and a recently introduced online minimum peak appointment scheduling problem. The high level…
Constraint satisfaction problems (CSPs) models many important intractable NP-hard problems such as propositional satisfiability problem (SAT). Algorithms with non-trivial upper bounds on running time for restricted SAT with bounded clause…
We revisit the classic #Knapsack problem, which asks to count the Boolean points $(x_1,\dots,x_n)\in\{0,1\}^n$ in a given half-space $\sum_{i=1}^nW_ix_i\le T$. This #P-complete problem admits $(1\pm\epsilon)$-approximation. Before this…
Many real-world optimization problems have multiple interacting components. Each of these can be NP-hard and they can be in conflict with each other, i.e., the optimal solution for one component does not necessarily represent an optimal…
The 0/1 multidimensional knapsack problem is the 0/1 knapsack problem with m constraints which makes it difficult to solve using traditional methods like dynamic programming or branch and bound algorithms. We present a genetic algorithm for…
This article details the algorithmics in FLSSS, an R package for solving various subset sum problems. The fundamental algorithm engages the problem via combinatorial space compression adaptive to constraints, relaxations and variations that…
Semi-online algorithms that are allowed to perform a bounded amount of repacking achieve guaranteed good worst-case behaviour in a more realistic setting. Most of the previous works focused on minimization problems that aim to minimize some…
The computational complexity of the partition, 0-1 subset sum, unbounded subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple variants were studied in numerous papers in the past where all the weights and profits were…
The hidden subgroup problem~(HSP) is one of the most important problems in quantum computation. Many problems for which quantum algorithm achieves exponential speedup over its classical counterparts can be reduced to the Abelian HSP.…
The Bilevel Optimization Problem is a hierarchical optimization problem with two agents, a leader and a follower. The leader make their own decisions first, and the followers make the best choices accordingly. The leader knows the…
The Map-Reduce computing framework rose to prominence with datasets of such size that dozens of machines on a single cluster were needed for individual jobs. As datasets approach the exabyte scale, a single job may need distributed…