相关论文: More Efficient Algorithms and Analyses for Unequal…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
A rateless code encodes a finite length information word into an infinitely long codeword such that longer prefixes of the codeword can tolerate a larger fraction of errors. A rateless code achieves capacity for a family of channels if, for…
We investigate the ratio $\rho_{n,L}$ of prefix codes to all uniquely decodable codes over an $n$-letter alphabet and with length distribution $L$. For any integers $n\geq 2$ and $m\geq 1$, we construct a lower bound and an upper bound for…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
Consider a channel with a given input distribution. Our aim is to degrade it to a channel with at most L output letters. One such degradation method is the so called "greedy-merge" algorithm. We derive an upper bound on the reduction in…
We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
A text written using symbols from a given alphabet can be compressed using the Huffman code, which minimizes the length of the encoded text. It is necessary, however, to employ a text-specific codebook, i.e. the symbol-codeword dictionary,…
The minimum and maximum cuts of an undirected edge-weighted graph are classic problems in graph theory. While the Min-Cut Problem can be solved in P, the Max-Cut Problem is NP-Complete. Exact and heuristic methods have been developed for…
Conflict-avoiding codes (CACs) have been used in multiple-access collision channel without feedback. The size of a CAC is the number of potential users that can be supported in the system. A code with maximum size is called optimal. The use…
We study local computation algorithms (LCA) for maximum matching. An LCA does not return its output entirely, but reveals parts of it upon query. For matchings, each query is a vertex $v$; the LCA should return whether $v$ is matched -- and…
We discuss inequalities holding between the vocabulary size, i.e., the number of distinct nonterminal symbols in a grammar-based compression for a string, and the excess length of the respective universal code, i.e., the code-based analog…
Adaptive coding faces the following problem: given a collection of source classes such that each class in the collection has non-trivial minimax redundancy rate, can we design a single code which is asymptotically minimax over each class in…
A common complaint about adaptive prefix coding is that it is much slower than static prefix coding. Karpinski and Nekrich recently took an important step towards resolving this: they gave an adaptive Shannon coding algorithm that encodes…
We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length…
The Automatic Amortized Resource Analysis (AARA) derives program-execution cost bounds using types. To do so, AARA often makes use of cost-free types, which are critical for the composition of types and cost bounds. However, inferring…
A perfect matching in an undirected graph $G=(V,E)$ is a set of vertex disjoint edges from $E$ that include all vertices in $V$. The perfect matching problem is to decide if $G$ has such a matching. Recently Rothvo{\ss} proved the striking…
There is a class of entropy-coding methods which do not substitute symbols by code words (such as Huffman coding), but operate on intervals or ranges. This class includes three prominent members: conventional arithmetic coding, range…
We introduce alphabet-permutation (AP) codes, a new family of error-correcting codes defined by iteratively applying random coordinate-wise permutations to a fixed initial word. A special case recovers random additive codes and random…