Joel I. Seiferas

THE SMALLEST AUTOMATON RECOGNIZING THE SUBWORDS OF A TEXT

Let a partial deterministic finite automaton be a DFA in which each state need not have a transition edge for each letter of the alphabet. We demonstrate that the smallest partial DFA for the set of all subwords of a given word w, Iwl>2, has at most 21w(-2 states and 3(wl-4 transition edges, independently of the alphabet size. We give an algorithm to build this smallest partial DFA from the input w on-line in linear time.

Time-space-optimal string matching

Abstract Any string-matching algorithm requires at least linear time and a constant number of local storage locations. We design and analyze an algorithm which realizes both asymptotic bounds simultaneously. This can be viewed as completely eliminating the need for the tabulated “failure function” in the linear-time algorithm of Knuth, Morris, and Pratt. It makes possible a completely general implementation as a Fortran subroutine or even as a six-head finite automaton.

Efficient and Elegant Subword-Tree Construction

A clean version of Weiner’s linear-time compact-subword-tree construction simultaneously also constructs the smallest deterministic finite automaton recognizing the reverse subwords.

An information-theoretic approach to time bounds for on-line computation

Abstract Static, descriptional complexity (program size) can be used to obtain lower bounds on dynamic, computational complexity (such as running time). We discuss the approach and use it to obtain lower time bounds for on-line simulation of one abstract storage unit by another. Our main results show that more points of access into multidimensional or tree-shaped storage can save significant time.

Non-uniform random membership management in peer-to-peer networks

Existing random membership management algorithms provide each node with a small, uniformly random subset of global participants. However, many applications would benefit more from non-uniform random member subsets. For instance, non-uniform gossip algorithms can provide distance-based propagation bounds and thus information can reach nearby nodes sooner. In another example, Kleinberg shows that networks with random long-links following distance-based non-uniform distributions exhibit better routing performance than those with uniformly randomized topologies. In this paper, we propose a scalable non-uniform random membership management algorithm, which provides each node with a random membership subset with application-specified probability e.g., with probability inversely proportional to distances. Our algorithm is the first non-uniform random membership management algorithm with proved convergence and bounded convergence time. Moreover, our algorithm does not put specific restrictions on the network topologies and thus has wide applicability.

The Convergence-Guaranteed Random Walk and Its Applications in Peer-to-Peer Networks

Network structure construction and global state maintenance are expensive in large-scale dynamic peer-to-peer (P2P) networks. With inherent topology independence and low state maintenance overhead, random walk is an excellent tool in such network environments. However, the current uses are limited to unguided or heuristic random walks with no guarantee on their converged node visitation probability distribution. Such a convergence guarantee is essential for strong analytical properties and high performance of many P2P applications. In this paper, we investigate an approach for random walks to converge to application-desired node visitation probability distributions while only requiring information about the direct neighbors of each peer. Our approach is guided by the Metropolis-Hastings algorithm for Monte Carlo Markov Chain sampling. Our contributions are threefold. First, we analyze the convergence time of the random walk node visitation probability distribution on common P2P network topologies. Second, we analyze the fault tolerance of our random walks in dynamic networks with potential walker losses. Third, we present the effectiveness of random walks in assisting three realistic network applications: random membership subset management, search, and load balancing. Both search and load balancing desire random walks with biased node visitation distributions to achieve application-specific goals. Our analysis, simulations, and Internet experiment demonstrate the advantage of our random walks compared with alternative topology-independent index-free approaches.

A note on almost-everywhere-complex sets and separating deterministic-time-complexity classes

Abstract For each time bound T: {input strings} → {natural numbers} that is some machines exact running time, there is a {0, 1}-valued function fT that can be computed within time proportional to T, but that cannot be computed within any time bound T′ that is infinitely often significantly smaller than T ( T′ ≠ Ω(T) , typically). Equivalently, every algorithm to compute fT requires time T′ on almost every input if T′ is almost everywhere significantly smaller than T (T′ = o(T), typically).

Refinements of the nondeterministic time and space hierarchies

We give sufficient conditions for NTIME(T , ) ~ NTIME(T2) and NSPACE(Sl) 1 NSPACE(S2)· These resul ts extend those of Cook [31 and Ibarra [81, respectively. We actually conclude that NTIME(T1) 1 2 in some cases where it is unknown whether DTIME(T 1 ) 1 DTIME(T2). Our results for space allow us to settle a question raised by Ibarra [9), thus completing his proof that nondeterministic two-way finite automata with k+2 heads accept more languages than those with only k heads.

A Tight Lower Bound for On-line Monotonic List Labeling

Maintaining a monotonic labeling of an ordered list during the insertion of n items requires \Omega (n log n) individual relabelings in the worst case, if the number of usable labels is only polynomial in n. This follows from a lower bound for a new problem, prefix bucketing.

Limitations on Separating Nondeterministic Complexity Classes

If the time bounds defining two nondeterministic complexity classes are too close for separation by the two known techniques, then they are almost too close for separation by any relativizable technique. Proof of an analogous result for space would be a major breakthrough, implying