Related papers: Linear time Constructions of some $d$-Restriction …
Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two…
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
Clause sets saturated by hierarchic ordered resolution do not offer a model representation that can be effectively queried, in general. They only offer the guarantee of the existence of a model. We present an effective symbolic model…
We give a new general approach for designing exact exponential-time algorithms for subset problems. In a subset problem the input implicitly describes a family of sets over a universe of size n and the task is to determine whether the…
We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for…
We give a general account of family algebras over a finitely presented linear operad, this operad together with its presentation naturally defining an algebraic structure on the set of parameters.
These lecture notes show that linear probing takes expected constant time if the hash function is 5-independent. This result was first proved by Pagh et al. [STOC'07,SICOMP'09]. The simple proof here is essentially taken from [Patrascu and…
Hashing with linear probing dates back to the 1950s, and is among the most studied algorithms. In recent years it has become one of the most important hash table organizations since it uses the cache of modern computers very well.…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
In the paper "Linear time algorithm to cover and hit a set of line segments optimally by two axis-parallel squares", TCS Volume 769 (2019), pages 63--74, the LHIT problem is proposed as follows: For a given set of non-intersecting line…
We propose a new family of constraints which combine together lexicographical ordering constraints for symmetry breaking with other common global constraints. We give a general purpose propagator for this family of constraints, and show how…
In the first part of this paper we introduced an algorithm that uses reachable set approximation to approximate the minimum time function of linear control problems. To illustrate the error estimates and to demonstrate differences to other…
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
In this paper, we bound the rate of linear codes in $\mathbb{F}_q^n$ with the property that any $k\leq q$ codewords are all simultaneously distinct in at least $d_k$ coordinates. For the case of particular interest $q=k=3$ we recover, with…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
In this paper we consider discrete time stochastic optimal control problems over infinite and finite time horizons. We show that for a large class of such problems the Taylor polynomials of the solutions to the associated Dynamic…
For any particular class of graphs, algorithms for computational problems restricted to the class often rely on structural properties that depend on the specific problem at hand. This begs the question if a large set of such results can be…
We construct two new families of linear codes by modifying the generator matrices of generalized Reed-Solomon (GRS) codes. For these codes, we explicitly derive parity-check matrices and establish necessary and sufficient conditions…
We show how to reduce the problem of solving members of a certain family of nonlinear differential equations to that of solving some corresponding linear differential equations.