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We show that in the quantum query model the complexity of detecting a triangle in an undirected graph on $n$ nodes can be done using $O(n^{1+{3\over 7}}\log^{2}n)$ quantum queries. The same complexity bound applies for outputting the…
We consider the following generalization of the classic Binary Search Problem: a searcher is required to find a hidden target vertex $x$ in a graph $G$, by iteratively performing queries about vertices. A query to $v$ incurs a cost $c(v,…
Motion planning problems can be simplified by admissible projections of the configuration space to sequences of lower-dimensional quotient-spaces, called sequential simplifications. To exploit sequential simplifications, we present the…
The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of…
Preference restrictions have played a significant role in computational social choice. This paper studies a framework that connects preference restrictions with classical graph search paradigms. We model candidates as vertices of a graph…
Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size~$N$ and margin~$\gamma$ (how well the given data are separated), the query complexity of the best-known…
Efficient index structures for fast approximate nearest neighbor queries are required in many applications such as recommendation systems. In high-dimensional spaces, many conventional methods suffer from excessive usage of memory and slow…
We study a game theoretic model where a coalition of processors might collude to bias the outcome of the protocol, where we assume that the processors always prefer any legitimate outcome over a non-legitimate one. We show that the problems…
We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…
We analyse the role of degree of entanglement for Vaidman's game in a setting where the players share a set of partially entangled three-qubit states. Our results show that the entangled states combined with quantum strategies may not be…
We present an algorithm that, with high probability, generates a random spanning tree from an edge-weighted undirected graph in $\tilde{O}(n^{4/3}m^{1/2}+n^{2})$ time (The $\tilde{O}(\cdot)$ notation hides $\operatorname{polylog}(n)$…
A tournament is a complete directed graph. It is well known that every tournament contains at least one vertex v such that every other vertex is reachable from v by a path of length at most 2. All such vertices v are called *kings* of the…
This paper is concerned with complexity theoretic aspects of a general formulation of quantum game theory that models strategic interactions among rational agents that process and exchange quantum information. In particular, we prove that…
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
A simple game $(N,v)$ is given by a set $N$ of $n$ players and a partition of~$2^N$ into a set~$\mathcal{L}$ of losing coalitions~$L$ with value $v(L)=0$ that is closed under taking subsets and a set $\mathcal{W}$ of winning coalitions $W$…
We introduce a `concrete complexity' model for studying algorithms for matching in bipartite graphs. The model is based on the "demand query" model used for combinatorial auctions. Most (but not all) known algorithms for bipartite matching…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…
This paper studies complexity theoretic aspects of quantum refereed games, which are abstract games between two competing players that send quantum states to a referee, who performs an efficiently implementable joint measurement on the two…
Quantum walks on binary trees are used in many quantum algorithms to achieve important speedup over classical algorithms. The formulation of this kind of algorithms as quantum circuit presents the advantage of being easily readable,…
In Exact Quantum Query model, almost all of the Boolean functions for which non-trivial query algorithms exist are symmetric in nature. The most well known techniques in this domain exploit parity decision trees, in which the parity of two…