This work concerns the mechanism design for online scheduling in a strategic setting. In this setting, each job is owned by a self-interested agent who may misreport the release time, deadline, length, and value of her job, while we need to determine not only the schedule of the jobs, but also the payment of each agent. We focus on the design of incentive compatible (IC) mechanisms, and study the maximization of social welfare (i.e., the aggregated value of completed jobs) by competitive analysis. We first derive two lower bounds on the competitive ratio of any deterministic IC mechanism to characterize the landscape of our research: one bound is 5, which holds for equal-length jobs; the other bound is $\frac{\kappa}{\ln\kappa}+1-o(1)$, which holds for unequal-length jobs, where $\kappa$ is the maximum ratio between lengths of any two jobs. We then propose a deterministic IC mechanism and show that such a simple mechanism works very well for two models: (1) In the preemption-restart model, the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal ratio of $(\frac{1}{(1-\epsilon)^2}+o(1)) \frac{\kappa}{\ln\kappa}$ for unequal-length jobs, where $0<\epsilon<1$ is a small constant; (2) In the preemption-resume model, the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal competitive ratio (within factor 2) for unequal-length jobs.

This study describes a novel feed‐forward segmented digital automatic gain control (FSD‐AGC) algorithm for long term evolution (LTE) digital radio‐over‐fibre (DRoF) systems. It experimentally demonstrates the algorithm using a DRoF platform based on real‐time field programmable gate arrays. The FSD‐AGC algorithm is able to update power status accurately with a short delay (about 100 samples) and adjust the gain precisely by only one step. It can make full use of analogue‐to‐digital converter quantisation bits width without oversaturation and maintain a stable peak‐to‐average ratio to reduce the overall cost and energy consumption of digital links and to minimise the deterioration of error vector magnitude (EVM) in LTE systems. Compared with conventional solutions, the proposed algorithm shows significant improvement in the dynamic range (a 20 dB improvement is demonstrated experimentally) of 4G‐LTE radio frequency signals in a DRoF system. This is a major step forward for the future commercialisation of DRoF systems for 4G and 5G network deployments. Meanwhile, FSD‐AGC can be applied in both LTE time division duplexing and frequency division duplexing signals. Experimental results have shown a mean EVM of the DRoF system below 4.5%, which is well below the 8% required by 3rd generation partnership project.

This paper concerns the mechanism design for online scheduling in a strategic setting. In this setting, each job is owned by a self-interested agent who may misreport the release time, deadline, length, and value of her job, while we need to determine not only the schedule of the jobs, but also the payment of each agent. We focus on the design of incentive compatible (IC) mechanisms, and study the maximization of social welfare (i.e., the aggregated value of completed jobs) by competitive analysis. We first derive two lower bounds on the competitive ratio of any deterministic IC mechanism to characterize the landscape of our research. We then propose a deterministic IC mechanism and show that such a simple mechanism works very well for both the preemption-restart model and the preemption-resume model. We show the mechanism can achieve the optimal competitive ratio of 5 for equal-length jobs and a near optimal competitive ratio (within a constant factor) for unequal-length jobs.

Given a preference system $(G, \prec)$ and an integral weight function defined on the edge set of $G$ (not necessarily bipartite), the maximum-weight stable matching problem is to find a stable matching of $(G, \prec)$ with maximum total weight. In this paper we study this $NP$-hard problem using linear programming and polyhedral approaches. We show that the Rothblum system for defining the fractional stable matching polytope of $(G, \prec)$ is totally dual integral if and only if this polytope is integral if and only if $(G, \prec)$ has a bipartite representation. We also present a combinatorial polynomial-time algorithm for the maximum-weight stable matching problem and its dual on any preference system with a bipartite representation. Our results generalize Király and Pap's theorem on the maximum-weight stable-marriage problem and rely heavily on their work.

Given a wired network of processors, and a source node that needs to broadcast a message to all other processors in the network, the minimum broadcast time problem is to find a scheme that accomplishes the broadcast in a minimum number of time rounds under the constraint that at each time round, no processor can forward the received message to more than one of its neighbors in the network. This NP-hard problem has been extensively studied in literatures. In this paper we focus on a variant of the minimum broadcast time problem: the minimum multicast time problem in wireless sensor networks under collision-free data transmission model. The goal of the problem is to multicast a message from the source node to a set of destination nodes in a minimum number of time rounds. This problem remains NP-hard even in the Euclidean plane and the current best approximation algorithm has performance ratio of 41. In this paper we propose a new algorithm that has performance ratio of 15.

We present a structural characterization of all tournaments $T=(V,A)$ such that, for any nonnegative integral weight function defined on V, the maximum size of a feedback vertex set packing is equal to the minimum weight of a triangle in T. We also answer a question of Frank by showing that it is $NP$-complete to decide whether the vertex set of a given tournament can be partitioned into two feedback vertex sets. In addition, we give exact and approximation algorithms for the feedback vertex set packing problem on tournaments.

Obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) construction is an essential part of routing. Recently, IC routing and related researches have been extended from Manhattan architecture (lambda2-geometry) to Y-/X-architecture (lambda3-lambda4-geometry) to improve the chip performance. This paper presents an O(n log n) heuristic, lambda-OAT, for obstacle-avoiding Steiner minimal tree construction in the lambda-geometry plane (lambda-OASMT). In this paper, based on obstacle-avoiding constrained Delaunay triangulation, a full connected tree is constructed and then embedded into lambda-OASMT by zonal combination. To the best of our knowledge, this is the first work addressing the lambda-OASMT problem. Compared with most recent works on OARSMT problem, lambda-OAT obtains up to 30-Kx speedup with quality solution. We have tested randomly generated cases with up to 10 K terminals and 10-K rectilinear obstacles within 4 seconds on a Sun V880 workstation (755-MHz CPU and 4-GB memory). The high efficiency and accuracy of lambda-OAT make it extremely practical and useful in the routing phase.

In recent years, the X-architecture is introduced to obtain better performance for integrated circuit physical design. This paper reformulates the global routing problem in X-architecture under the liquid routing model. Then, a dynamic resource assignment (Dra) method is presented to reduce potential vias. At last, a global router called DraXRouter, is designed, in which we adopt a dynamic-tabulist-based tree construction algorithm and a stochastic optimization strategy to gain high quality routing solution. Tested on ISPD'98 benchmarks, DraXRouter achieves better routing performance compared with two recent global routers.

The X-architecture is a new integrated-circuit wiring technique in the physical design. Compared with the currently used M-architecture, which uses either horizontal or vertical routing, it is based on the pervasive use of diagonal wires. The experimental studies show that the X-architecture demonstrates a wire length reduction of more than 10-20% and better performance of timing. In this paper, we make a theoretical study on the wire lengths under these two architectures and obtain their expected values for the cases of two and three terminals, respectively. Our theoretical study confirms the wire length reduction as previous experimental studies claimed, but the reduction for three terminals is not as significant as for two terminals. Our analysis shows that the wire length reduction tends to become smaller as the number of terminals turns larger. We also estimate the lower and upper bounds on the expected wire lengths of M-architecture and X-architecture for arbitrary number of terminals.

Routing is one of the important phases in VLSI/ULSI physical design. The obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) construction is an essential part of routing since macro cells, IP blocks, and pre-routed nets are often regarded as obstacles in the routing phase. Efficient OARSMT algorithms can be employed in practical routers iteratively. Recently, IC routing and related researches have been extended from Manhattan architecture (λ2-geometry) to Y- / X-architecture (λ3- / λ4-geometry) to improve the chip performance. This paper presents an O(nlogn) heuristic, λ-OASMT, for obstacle-avoiding Steiner minimal tree construction in the λ-geometry plane. Based on obstacle-avoiding constrained Delaunay triangulation, a full connected tree is constructed and then embedded into λ-OASMT by a novel method called zonal combination. To the best of our knowledge, this is the first work addressing the λ-OASMT problem. Compared with two most recent works on OARSMT problem, λ-OASMT obtains up to 30Kx speedup with an even better quality solution. We have tested randomly generated cases with up to 1K terminals and 10K rectilinear obstacles within 3 seconds on a Sun V880 workstation (755MHz CPU and 4GB memory). The high efficiency and accuracy of λ-OASMT make it extremely practical and useful in the routing phase, as well as interconnect estimation in the process of floorplanning and placement.

CAD tools have become more and more important for integrated circuit (IC) design since a complicated system can be designed into a single chip, called system-on-a-chip (SOC), in which physical design tool is an essential and critical part. We try to consider the via minimization problem as early as possible in physical design. We propose a routing method focusing on minimizing vias while considering mutability and wire-length constraint. That is, in the global routing phase, we minimize the number of bends, which is closely related to the number of vias. Previous work only dealt with very small nets, but our algorithm is general for the nets with any size. Experimental results show that our algorithm can greatly reduce the count of bends for various sizes of nets while meeting the constraints of congestion and wire-length.

Routing is one of the important steps in VLSI/ULSI physical design. The rectilinear Steiner minimum tree (RSMT) construction is an essential part of routing. Since macro cells, IP blocks, and pre-routed nets are often regarded as obstacles in the routing phase, obstacle-avoiding RSMT (OARSMT) algorithms are useful for practical routing applications. This paper focuses on the OARSMT problem and presents an algorithm, named An-OARSMan, based on ant colony optimization. A greedy obstacle penalty distance (OP-distance) local heuristic is used in the algorithm and performed on the track graph. The algorithm has been implemented and tested on different kinds of obstacles. Experimental results show that An-OARSMan can handle complex obstacle cases including both convex and concave polygon obstacles with good length performance. It can always achieve the optimal solution in the cases with no more than 7 terminals.

Motivated by VLSI/ULSI routing applications, we present a heuristic for rectilinear Steiner minimal tree (RSMT) construction. We transform a rectilinear minimum spanning tree (RMST) into an RSMT by a novel method called polygonal contraction. Experimental results show that the heuristic matches or exceeds the solution quality of previously best known algorithms and runs much faster.

In WDM networks with limited drop-offs, the route of a multicast connection consists of a set of light-trees. Each of the light-tree is rooted at the source node and contains no more than a limited number, say k, destination nodes due to the power loss of dropping optical signals off at destination nodes. We call such a light-tree k-drop light-tree. In this paper we study the multicast routing problem of constructing a set of k-drop light-trees that have the minimal network cost. The network cost of a set of light-trees is defined as the summation of the link cost of all the light-trees. We first prove that this problem is polynomial-time solvable for k=2 and NP-hard for k/spl ges/3. We then propose a 4-approximation algorithm for the problem for k /spl ges/3. A wavelength assignment algorithm is also proposed to assign wavelengths to the light-trees of a multicast connection. In the end we give simulation results showing that k-drop multitree muting can significantly save not only the network cost but also wavelengths used. Moreover, when k/spl ges/5 its performance is very close to the case where k is infinite (i.e., the case of using a single tree for a multicast connection).

This paper investigates the optimal placement of proxies of a Web server on the Internet, with the consideration of both read and update operations to the data on the Web server. We first study the problem of optimal placement of $k$ proxies in a system to minimize the total access cost to the Web server. Then, for an unknown number of proxies, we find the optimal number of proxies required in the system. The problems are formulated by using the dynamic programming method and the optimal solutions are obtained. Simulations have been conducted to evaluate the performance of the proposed algorithms and to demonstrate how the effectiveness of proxy placement is affected by various factors, such as network traffic load, number of proxies, read–write ratio and proxy hit ratio.

An important goal of the design of WDM (wavelength division multiplexing) networks is to use less wavelengths to serve more communication needs. According to the wavelength conflict rule, we know that the number of wavelengths required in a WDM network is at least equal to the maximal number of channels over a fiber (called maximal link load) in the network. By placing wavelength converters at some nodes in the network, the number of wavelengths needed can be made equal to the maximal link load. In this paper we study the problem of placing the minimal number of converters in a network to achieve that the number of wavelengths in use is equal to the maximal link load. For duplex communication channels, we prove that an optimal solution can be obtained in polynomial-time. For unidirectional communication channels, which was proved to be NP-complete, we develop a set of lemmas which lead to an efficient approximation algorithm whose approximation ratio is two.

This paper investigates the optimal placement of proxies of a Web server on the Internet. With the consideration of both read and write operations to the data on the Web server. First, we study the problem of optimal placement of k proxies in a system to minimize the total access cost to the Web server. Then, for unknown number of proxies, we find the optimal number of proxies required in the system. The problems are formulated using a dynamic programming method and optimal solutions are obtained. Intensive simulations have been conducted to evaluate the performance of the proposed algorithms, and to demonstrate the relationship between the number of proxies required in the system and the read-write ratio. This work can significantly alleviate the Web access traffic on the Internet and improve the performance of the Web server.

This paper investigates the issues of the optimal placement of a limited number of Web proxies in an environment where a Web site is replicated (i.e. mirrored Web sites). Two different objectives are studied: minimizing the overall access cost by all clients to the Web site and minimizing the longest delay for any client to access the Web site. The problem is reduced to the placement of proxies in a set of trees whose root nodes are the server replicas. It is then formulated and solved by using a dynamic programming method. The significance of this work includes: (1) alleviating the Internet traffic of Web accesses; (2) improving the response time of Web page accesses; (3) maximizing Web server performance by using a limited number of proxies.

Given a WDM optical network with wavelength channels on its fiber links, we consider the problem of finding the minimum set of network nodes such that, with wavelength converters at these nodes, broadcast can be supported in the network. We call this problem the converter placement problem. We model a given network using a graph G with colors on its edges and give a mathematical formulation for the problem based on the graph model. Two related problems, color-covering and vertex color-covering, are given and analyzed. Both of them are shown to have a polynomial-time approximation with performance ratio ln n+1 and ln n is the best possible performance ratio unless NP /spl sub/ DTIME(n/sup poly log n/), where n is the number of vertices in G. Using these results, we show that the Converter Placement problem has a polynomial-time approximation with performance ratio 2(ln n+1) and 1/2 ln n is the best possible performance ratio unless NP /spl sub/ DTIME(n/sup poly log n/). We present an approximation algorithm to solve the converter placement problem and study the performance of the algorithm on randomly generated network topologies.

This paper discusses quality-of-service (QoS) multicast in wavelength-division multiplexing (WDM) networks. Given a set of QoS multicast requests, we are to find a set of cost suboptimal QoS routing trees and assign wavelengths to them. The objective is to minimize the number of wavelengths in the system. This is a challenging issue. It involves not only optimal QoS multicast routing, but also optimal wavelength assignment. Existing methods consider channel setup in WDM networks in two separate steps: routing and wavelength assignment, which has limited power in minimizing the number of wavelengths. In this paper, we propose a new optimization method, which integrates routing and wavelength assignment in optimization of wavelengths. Two optimization algorithms are also proposed in minimizing the number of wavelengths. One algorithm minimizes the number of wavelengths through reducing the maximal link load in the system; while the other does it by trying to free out the least used wavelengths. Simulation results demonstrate that the proposed algorithms can produce suboptimal QoS routing trees and substantially save the number of wavelengths.

In multihop systems of wavelength division multiplexing (WDM) networks, wavelength conversion is required at the conjunction of two lightpaths if they use different wavelengths. We consider the problem of assigning wavelengths to the lightpaths by using a limited number of wavelengths, so that the overall number of wavelength conversions in the whole system is minimal. The problem is formulated as a maximum clique cover problem. An approximation algorithm is proposed to solve it. Our proposed theory also illustrates the tradeoff relationship between the number of wavelengths and the number of conversions in the system.

Investigates the issues of placing a limited number of Web proxies in an environment where the Web server is replicated (i.e. mirrored Web servers). Two different objectives are considered: (a) minimizing the overall access cost by all clients of the Web server, and (b) minimizing the longest delay for any client to access the Web server. The problems are formulated and solved by using a dynamic programming method. This work can: (1) alleviate the amount of Internet traffic incurred by fast-growing Web accesses; (2) improve the response time of Web server accesses; and (3) maximize Web server performance by using a limited number of proxies.

In a WDM network under multihop architecture, each link is associated with a set of wavelengths available for channel connections, and in the network, the number of wavelengths that can be used is limited. Data transmission over one wavelength to another requires wavelength conversion, which causes a long delay. Given a multicast connection, routing is to construct a tree for the connection that is rooted from the source and connects all destinations. In this paper, we consider the problem of constructing a routing tree with a minimal number of wavelengths on the tree. We first prove that this problem is NP-hard and then propose an approximation algorithm, which produces a routing tree that has not only a small number of wavelengths but also a short delay from the source to all destinations. © 2000 John Wiley & Sons, Inc.

Chung and Ross [SIAM J. Comput., 20 (1991), pp. 726--736] conjectured that the multirate three-stage Clos network C(n,2n-1,r) is rearrangeable in the general discrete bandwidth case; i.e., each connection has a weight chosen from a given finite set {p 1 , p 2 ,. . .,p k } where $1 \geq p_1 > p_2 > \cdots > p_k > 0$ and p i is an integer multiple of p i , denoted by $p_k \mid p_i$, for $1 \leq i \leq k-1$. In this paper, we prove that multirate three-stage Clos network C(n,2n-1,r) is rearrangeable when each connection has a weight chosen from a given finite set {p 1 , p 2 ,. . .,p k } where $1 \geq p_1 > p_2 > \cdots > p_{h} > 1/2 \geq p_{h+1} > \cdots > p_k > 0$ and p h+2 | p h+1 ,p h+3 |p h+2 ,. . . ,p k | p h+1 . We also prove that C(n,2n-1,r) is two-rate rearrangeable and $C(n, \lceil \frac{7n}{3} \rceil, r)$ is three-rate rearrangeable.

In this paper, we consider the problem of constructing the shortest two-connected Steiner network on the Euclidean plane. For a given set P of points on the Euclidean plane, let l2(P) denote the length of the shortest two-connected Steiner network on P divided by the length of the shortest two-connected spanning network on P. We prove that l2(P) = 1, if any one of the following conditions is satisfied: (1) All points in P are on the sides of the convex hull of P; (2) all points except one in P are on the sides of the convex hull of P; or (3) the cardinality of P is no greater than 5. Moreover, we obtain general lower and upper bounds for l2(P) as follows: (√3/2) ≤ inf{l2(P) | P} ≤ [(√3 + 2)/(√3 + 6)]. We also show that Christofides' heuristic for the traveling salesman problem can be used to design a polynomial-time algorithm for finding the shortest two-connected Steiner and spanning network with guaranteed worst-case performance ratio of √3 and 3/2;, respectively. © 1998 John Wiley & Sons, Inc. Networks 32: 133–140, 1998

A double-loop network with hop constants h1, h2, DL(n, h1, h2) may be represented as a directed graph with n nodes 0, 1, …, n − 1 and 2n links of the form i → i + h1mod n and i → i + h2mod n (referred to as h1-links and h2-links). They have been proposed as architectures for local area networks and for data alignment in SIMD processors, among other applications. Three reliability models of double-loop networks have been studied in the literature. In the link model, nodes always work and each link fails independently with probability p. Hwang and Li showed that for p small DL(n, 1, 1 + n/2) is most reliable for n even, and DL(n, 1, 2) is most reliable for n odd. In the node model, links always work and each node fails independently with probability p. Hu et al. showed that for p small DL(n, 1, 1 + ⌈n/2⌉) is the most reliable. However, no nonenumerative algorithms were given to compute the reliabilities of these most reliable networks except DL(n, 1, 1 + n/2) for even n under the node model. Recently, Hwang and Wright proposed a novel approach to compute the reliabilities of double-loop networks under the uniform model that each node fails with probability p, each h1-link with probability p1, and each h2-link with probability p2, and the failures are independent. In particular, they obtained the reliabilities for DL(n, 1, 2). In this paper, we applied their approach to compute the reliabilities of DL(n, 1, 1 + ⌈n/2⌉) under the uniform model, except that for n odd we need the assumption that h1-links always work. Note that even under this additional assumption our reliability model is more general than is the node model, the original model under which DL(n, 1, 1 + ⌈n/2⌉) is found to be most reliable for n odd. We also used this approach to obtain the reliabilities of DL(n, 1, n − 2), known as the daisy chain in the literature. © 1997 John Wiley & Sons, Inc. Networks 30: 81–90, 1997

Abstract Double loop networks have been intensively studied as interconnecting networks. However, the reliability analysis of such networks has hit a snag since the usual measure of reliability, the graph connectivity, is completely powerless as all double loops, if connected, are 2‐connected. Recently, Hwang and Li introduced a new analysis by partitioning cutsets into isolated and nonisolated ones and gave results on both types. Along the same line, we extent their results to the survival reliability model by showing that when each node fails independently with a very small probability, G(1, 1 + [n/2]) is the most reliable connected double loop network except when n = 3 and 9, in which case G(1, 2) is the most reliable. © 1993 by John Wiley & Sons, Inc.

Abstract A chordal ring is a degree‐3 regular graph with n vertices on a ring and n/2 chords determined by a parameter h. Chordal rings are attractive as topologies for computer networks due to their simple structures and short diameters. In this work, we study the reliabilities of chordal rings assuming each edge can independently fail with probability p. For p small, the usual criterion to measure the reliability of a network is its line‐connectivity. We show that all chordal rings have the same line‐connectivity and the same super line‐connectivity. We analyze the reliabilities of chordal rings by using the recently developed notions of isolated and nonisolated cutsets and list the optimal choices of h for n ≤ 30.