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Longest common substring (LCS), longest palindrome substring (LPS), and Ulam distance (UL) are three fundamental string problems that can be classically solved in near linear time. In this work, we present sublinear time quantum algorithms…
The problem of maximizing the average rate in a multicast network subject to a coverage constraint (minimum quality of service) is studied. Assuming the channel state information is available only at the receiver side and single antenna…
We consider computations over networks with multiple broadcast channels that intersect at a single party. Each broadcast link suffers from random bit-flip noise that affects the receivers independently. We design interactive coding schemes…
We study sketching and streaming algorithms for the Longest Common Subsequence problem (LCS) on strings of small alphabet size $|\Sigma|$. For the problem of deciding whether the LCS of strings $x,y$ has length at least $L$, we obtain a…
Sparse random linear network coding (SRLNC) used as a class of erasure codes to ensure the reliability of multicast communications has been widely investigated. However, an exact expression for the decoding success probability of SRLNC is…
It is a well-known result that constructing codewords over $GF(2)$ to minimize the number of transmissions for a single-hop wireless multicasting is an NP-complete problem. Linearly independent codewords can be constructed in polynomial…
This paper studies the problem of user association, scheduling and channel allocation in dense cellular networks with energy harvesting base stations (EBSs). In this problem, the EBSs are powered solely by renewable energy and each user has…
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…
A square coloring of a graph $G$ is a coloring of the square $G^2$ of $G$, that is, a coloring of the vertices of $G$ such that any two vertices that are at distance at most $2$ in $G$ receive different colors. We investigate the complexity…
Goemans and Rothvoss (SODA'14) gave a framework for solving problems which can be described as finding a point in int$.$cone$(P\cap\mathbb{Z}^N)\cap Q$, where $P,Q\subset\mathbb{R}^N$ are (bounded) polyhedra. The running time for solving…
This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set…
We consider the communication capacity of wireline networks for a two-unicast traffic pattern. The network has two sources and two destinations with each source communicating a message to its own destination, subject to the capacity…
Coded multicasting has been shown to improve the caching performance of content delivery networks with multiple caches downstream of a common multicast link. However, the schemes that have been shown to achieve order-optimal perfor- mance…
A novel class of achievable rate regions is obtained for the K-receiver broadcast channel with two groupcast messages. The associated achievability schemes are parameterized by an expansion of the message set which then determines how…
Randomized network coding (RNC) greatly reduces the complexity of implementing network coding in large-scale, heterogeneous networks. This paper examines two tradeoffs in applying RNC: The first studies how the performance of RNC varies…
Operators of networks covering large areas are confronted with demands from some of their customers who are virtual service providers. These providers may call for the connectivity service which fulfils the specificity of their services,…
We propose a simple yet effective wireless network coding and decoding technique. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by generator matrices of linear block…
We give a near-optimal quantum algorithm for the longest common substring (LCS) problem between two run-length encoded (RLE) strings, with the assumption that the prefix-sums of the run-lengths are given. Our algorithm costs…
This paper studies the 1-2-1 half-duplex network model, where two half-duplex nodes can communicate only if they point `beams' at each other; otherwise, no signal can be exchanged or interference can be generated. The main result of this…
This paper considers vector network coding based on rank-metric codes and subspace codes. Our main result is that vector network coding can significantly reduce the required field size compared to scalar linear network coding in the same…