Related papers: Knapsack problem for automaton groups

We consider a selfish variant of the knapsack problem. In our version, the items are owned by agents, and each agent can misrepresent the set of items she owns---either by avoiding reporting some of them (understating), or by reporting…

Ensemble-based approaches are very effective in various fields in raising the accuracy of its individual members, when some voting rule is applied for aggregating the individual decisions. In this paper, we investigate how to find and…

In this paper, we propose a unified framework and an algorithm for the problem of group recommendation where a fixed number of items or alternatives can be recommended to a group of users. The problem of group recommendation arises…

Subzero automata is a class of tree automata whose acceptance condition can express probabilistic constraints. Our main result is that the problem of determining if a subzero automaton accepts some regular tree is decidable.

We construct a class of finitely generated groups which have arbitrarily large conjugacy separability function, but in which the conjugacy problem can be solved in polynomial time, demonstrating that the McKinsey algorithm for the conjugacy…

Topological transitivity is a fundamental notion in topological dynamics and is widely regarded as a basic indicator of global dynamical complexity. For general cellular automata, topological transitivity is known to be undecidable. By…

This paper investigates the time-bounded version of the reachability problem for hybrid automata. This problem asks whether a given hybrid automaton can reach a given target location within T time units, where T is a constant rational…

We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…

Budget feasible mechanisms, recently initiated by Singer (FOCS 2010), extend algorithmic mechanism design problems to a realistic setting with a budget constraint. We consider the problem of designing truthful budget feasible mechanisms for…

There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…

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 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms…

We prove that the compressed word problem and the compressed simultaneous conjugacy problem are solvable in polynomial time in hyperbolic groups. In such problems, group elements are input as words defined by straight line programs defined…

This paper introduces a family of learning-augmented algorithms for online knapsack problems that achieve near Pareto-optimal consistency-robustness trade-offs through a simple combination of trusted learning-augmented and worst-case…

We show that there are Cayley automatic groups that are not Cayley biautomatic. In addition, we show that there are Cayley automatic groups with undecidable Conjugacy Problem and that the Isomorphism Problem is undecidable in the clas of…

This short note aims at proving that the isolation problem is undecidable for probabilistic automata with only one probabilistic transition. This problem is known to be undecidable for general probabilistic automata, without restriction on…

We construct an automaton group with a PSPACE-complete word problem, proving a conjecture due to Steinberg. Additionally, the constructed group has a provably more difficult, namely EXPSPACE-complete, compressed word problem and acts over a…

We introduce a new geometric tool for analyzing groups of finite automata. To each finite automaton we associate a square complex. The square complex is covered by a product of two trees iff the automaton is bi-reversible. Using this method…

We study finitely generated groups whose word problems are accepted by counter automata. We show that a group has word problem accepted by a blind n-counter automaton in the sense of Greibach if and only if it is virtually free abelian of…

The 0/1 knapsack problem is weakly NP-hard in that there exist pseudo-polynomial time algorithms based on dynamic programming that can solve it exactly. There are also the core branch and bound algorithms that can solve large randomly…