Related papers: On a Communication Complexity problem in Combinato…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
The subject of this paper is the time complexity of approximating Knapsack, Subset Sum, Partition, and some other related problems. The main result is an $\widetilde{O}(n+1/\varepsilon^{5/3})$ time randomized FPTAS for Partition, which is…
We prove that the power word problem for certain metabelian subgroups of $\mathsf{GL}(2,\mathbb{C})$ (including the solvable Baumslag-Solitar groups $\mathsf{BS}(1,q) = \langle a,t \mid t a t^{-1} = a^q \rangle$) belongs to the circuit…
We consider the distributed version of the Multiple Knapsack Problem (MKP), where $m$ items are to be distributed amongst $n$ processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff…
Sequence partition problems arise in many fields, such as sequential data analysis, information transmission, and parallel computing. In this paper, we study the following partition problem variant: given a sequence of $n$ items…
The Time-Invariant Incremental Knapsack problem (IIK) is a generalization of Maximum Knapsack to a discrete multi-period setting. At each time, capacity increases and items can be added, but not removed from the knapsack. The goal is to…
Knapsack problems (KPs) are common in industry, but solving KPs is known to be NP-hard and has been tractable only at a relatively small scale. This paper examines KPs in a slightly generalized form and shows that they can be solved nearly…
The task of the broadcast problem is, given a graph G and a source vertex s, to compute the minimum number of rounds required to disseminate a piece of information from s to all vertices in the graph. It is assumed that, at each round, an…
Many combinatorial problems involving weights can be formulated as a so-called ranged problem. That is, their input consists of a universe $U$, a (succinctly-represented) set family $\mathcal{F} \subseteq 2^{U}$, a weight function $\omega:U…
In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum…
This work studies the combinatorial optimization problem of finding an optimal core tensor shape, also called multilinear rank, for a size-constrained Tucker decomposition. We give an algorithm with provable approximation guarantees for its…
We consider AC electrical systems where each electrical device has a power demand expressed as a complex number, and there is a limit on the magnitude of total power supply. Motivated by this scenario, we introduce the complex-demand…
We consider a group-theoretic analogue of the classic subset sum problem. It is known that every virtually nilpotent group has polynomial time decidable subset sum problem. In this paper we use subgroup distortion to show that every…
Graph clustering is the problem of identifying sparsely connected dense subgraphs (clusters) in a given graph. Proposed clustering algorithms usually optimize various fitness functions that measure the quality of a cluster within the graph.…
The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…
We study a constrained version of the knapsack problem in which dependencies between items are given by the adjacencies of a graph. In the 1-neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also…
Online knapsack problem is considered, where items arrive in a sequential fashion that have two attributes; value and weight. Each arriving item has to be accepted or rejected on its arrival irrevocably. The objective is to maximize the sum…
We study nondeterministic communication complexity and related concepts (fooling sets, fractional covering number) of random functions $f\colon X\times Y \to \{0,1\}$ where each value is chosen to be 1 independently with probability…
This paper surveys the field of quantum communication complexity. Some interesting recent results are collected concerning relations to classical communication, lower bound methods, one-way communication, and applications of quantum…
We prove that persuasion is an NP-complete problem.