Related papers: Counting Matchings via Capacity Preserving Operato…
This paper is motivated by the question whether there exists a logic capturing polynomial time computation over unordered structures. We consider several algorithmic problems near the border of the known, logically defined complexity…
We present a new upper bound for the orders of derivatives in the Rosenfeld-Groebner algorithm. This algorithm computes a regular decomposition of a radical differential ideal in the ring of differential polynomials over a differential…
We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself is trivial, the method which we apply shows that in order to achieve capacity…
We consider the problem of estimating an upper bound on the capacity of a memoryless channel with unknown channel law and continuous output alphabet. A novel data-driven algorithm is proposed that exploits the dual representation of…
A super-stable matching, which was introduced by Irving, is a solution concept in a variant of the stable matching problem in which the preferences may contain ties. Irving proposed a polynomial-time algorithm for the problem of finding a…
One fundamental problem in the field of network coding is to determine the network coding capacity of networks under various network coding schemes. In this thesis, we address the problem with two approaches: matroidal networks and capacity…
Understanding the power of space-bounded computation with access to catalytic space has been an important theme in complexity theory over the recent years. One of the key algorithmic results in this area is that bipartite maximum matching…
The Parity Source Coder is a protocol for data compression which is based on a set of parity checks organized in a sparse random network. We consider here the case of memoryless unbiased binary sources. We show that the theoretical capacity…
This paper presents a new lower bound for the discrete strategy improvement algorithm for solving parity games due to Voege and Jurdziski. First, we informally show which structures are difficult to solve for the algorithm. Second, we…
We define a new congruence relation on the set of integers, leading to a group similar to the multiplicative group of integers modulo $n$. It makes use of a symmetry almost omnipresent in modular multiplications and halves the number of…
If $Au=-div(a(x,Du))$ is a monotone operator defined on the Sobolev space $W^{1,p}(R^n)$, $1<p<+\infty$, with $a(x,0)=0$ for a.e. $x\in R^n$, the capacity $C_A(E,F)$ relative to $A$ can be defined for every pair $(E,F)$ of bounded sets in…
We develop a systematic approach, based on convex programming and real analysis, for obtaining upper bounds on the capacity of the binary deletion channel and, more generally, channels with i.i.d. insertions and deletions. Other than the…
Deterministic identification (DI) has emerged as a promising paradigm for large-scale and goal-oriented communication systems. Despite significant progress, a fundamental open problem has remained unresolved: a persistent gap between the…
First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
Since its inception in the mid-60s, the inventory staggering problem has been explored and exploited in a wide range of application domains, such as production planning, stock control systems, warehousing, and aerospace/defense logistics.…
Given a text $T$ and a pattern $P$, the order-preserving matching problem is to find all substrings in $T$ which have the same relative orders as $P$. Order-preserving matching has been an active research area since it was introduced by…
We address the maximum attainable rate of fingerprinting codes under the marking assumption, studying lower and upper bounds on the value of the rate for various sizes of the attacker coalition. Lower bounds are obtained by considering…
A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…
Gaussian polynomial, which is also known as $q$-binomial coefficient, is one of the fundamental concepts in the theory of partitions. Zeilberger provided a combinatorial proof of Gaussian polynomial, which is called Algorithm Z by Andrews…